Matrix

Problem 501

MATh140 Second Firstsem-2024-2025, (161745)(-4) mentie
Question 8 of 18 A matrix that is both sympetric and upper triangular must be a diagonal matrix. True Falle

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Problem 502

Question 16 of 18 Let $A$ be $2 \times 2$ matrix with $\operatorname{det}(A)=-2$ , then $\operatorname{det}\left(4 A^{-1}\right)=$ 8 - 2 2 $1 / 8$

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Problem 503

Calculate $n$ using the formula $n = A \cdot B \times A C$ and the determinant $\left| \begin{array}{ccc} 3 & 1 & 1 \\ 2 & -1 & -3 \end{array} \right|$ .

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Problem 504

The weather on any given day in a particular city can be sunny, cloudy, or rainy. It has been observed to be predictable largely on the basis of the weather on the previous day. Specifically:
- if it is sunny on one day, it will be sunny the next day $\frac{1}{3}$ of the time, and be cloudy the next day $\frac{2}{3}$ of the time - if it is cloudy on one day, it will be sunny the next day $\frac{2}{3}$ of the time, and be cloudy the next day $\frac{1}{6}$ of the time - if it is rainy on one day, it will be sunny the next day $\frac{1}{6}$ of the time, and be cloudy the next day $\frac{1}{3}$ of the time
Using 'sunny', 'cloudy', and 'rainy' (in that order) as the states in a system, set up the transition matrix for a Markov chain to describe this system.
Use your matrix to determine the probability that it will rain on Thursday if it is sunny on Sunday.
$P=\left[\begin{array}{lll} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]$
Probability of rain on Thursday $=0$

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Problem 505

浙江科技大学考试试卷
4. The state of plane stress at a point with respect to the $x y$ -axes is shown in Figure. Determine the principal stresses and principal planes. Show the results on a sketch of an element aligned with the principal directions. (25 points）

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Problem 506

If $\left[\begin{array}{lll}3 & 7 & 1\end{array}\right] \cdot\left[\begin{array}{l}5 \\ 3 \\ 6\end{array}\right]=\left[x_{1}\right]$ , what is the value of $x_{1}$ ? If the matrix operation is not possible, write "none".

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Problem 507

Given matrix $A$ and vector $\mathbf{b}$ , determine if $\mathbf{b}$ is in the span of columns of $A$ . How many vectors are in this span?

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Problem 508

Given matrix $A$ and vector $b$ , check if $b$ is in the span of columns of $A$ . How many vectors are in the set?

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Problem 509

Given matrix $A$ and vector $b$ , determine if $b$ is in the span of columns of $A$ . How many vectors are in this span?

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Problem 510

Ms. Lowell's class has a decimal chart. Answer these:
5. What pattern do you see moving left to right?
6. How does the last square in each row differ?
7. What pattern do you observe moving down a column?

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Problem 511

Fill in the missing values in the table using totals. If unknown + 67 = 99, then unknown = 32. Total students who play sports and an instrument = 35.

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Problem 512

Temukan nilai eigen dan vektor eigen dan matriks A -3 3 3-5 3 6-64

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Problem 513

1. Temukan nilai eigen dan vektor eigen dari matriks $A=\left[\begin{array}{ccc}1 & -3 & 3 \\ 3 & -5 & 3 \\ 6 & -6 & 4\end{array}\right]$

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Problem 514

LATIHAN
1. Temukan nilai eigen dan vektor eigen dari matriks $A=\left[\begin{array}{ccc}1 & -3 & 3 \\ 3 & -5 & 3 \\ 6 & -6 & 4\end{array}\right]$
2. Temukan nilai eigen dan vektor eigen dari matriks $A=\left[\begin{array}{cc}0 & 1 \\ -2 & -3\end{array}\right]$

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Problem 515

Find the vector of stable probabilities for the Markov chain whose transition matrix is $\begin{array}{c} {\left[\begin{array}{ccc} 0.1 & 0.8 & 0.1 \\ 1 & 0 & 0 \\ 1 & 0 & 0 \end{array}\right]} \\ W= \end{array}$ $\square$ $\square$

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Problem 516

[4] If $A^{-1}=\left[\begin{array}{cc}3 & 2 \\ -1 & 1\end{array}\right]$ and $B^{-1}=\left[\begin{array}{cc}1 & -1 \\ -3 & 4\end{array}\right]$ , and $(A B)^{-1}=\left[\begin{array}{ll}x & z \\ y & h\end{array}\right]$ , then $x+y+z+h$ a) -10 b) 3 c) 8 d) 20 [5] If $\left|\begin{array}{cccc}a & b & c & d \\ e & f & g & h \\ i & j & k & l \\ m & n & o & p\end{array}\right|=-3$ , then $\operatorname{det}\left(2\left[\begin{array}{cccc}a & b & c & d \\ e & f & g & h \\ i & j & k & l \\ m & n & o & p\end{array}\right]\right)=$ a) -6 b) -48 c) -12 d) -32 [6] The linear system given by $A X=B$ where $A$ is $2 \times 2$ square matrix, $A_{x}=\left[\begin{array}{cc}2 & -1 \\ 6 & 1\end{array}\right]$ and $A_{y}=\left[\begin{array}{ll}3 & 2 \\ 1 & 6\end{array}\right]$ , then $X=$ a) $\left[\begin{array}{l}2 \\ 4\end{array}\right]$ b) $\left[\begin{array}{c}-2 \\ 4\end{array}\right]$ c) $\left[\begin{array}{l}4 \\ 2\end{array}\right]$ d) $\left[\begin{array}{l}-4 \\ -2\end{array}\right]$
Q2: Write (T) for the correct statement and (F) for the false one [1] $\qquad$ If $|A|=\left|A^{-1}\right|$ then $|A|$ must equal to 1. [2] $\qquad$ If $A=[-\sqrt{2}]$ then $A^{-1}=\left[-\frac{\sqrt{2}}{2}\right]$ [3] $\qquad$ $3 A^{\mathrm{T}} A$ is a symmetric matrix. [4] $\qquad$ The matrix $A=\left[\begin{array}{cccc}1 & 5 & -3 & 0 \\ 0 & -2 & 0 & 8 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & 2\end{array}\right]$ is singular.

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Problem 517

KEA CY PA-Common Core Mat 122.core.learn.edgenuity.com/player/ et bookmarks Edgenuity Scanlon PLC HR 6-74 Downloads HMH Central Login Is Is $\overline{W P}$ Home - William Pen Cool Math Games - Common Core Math 8 Q2 1 2 8 4 ( 8 6 7 8 9 10 TIMEREMAINING 58:47
The lunch coordinator is recording the drink choices of the students in her school. She has partially completed the table. Which describes the variables in the two-way table? \begin{tabular}{|c|c|c|c|} \hline \multicolumn{4}{|c|}{ Lunch Drinks } \\ \hline & Milk & Water & Total \\ \hline Girls & & 52 & 85 \\ \hline Boys & 41 & & 93 \\ \hline Total & & & \\ \hline \hline \end{tabular} gender and number who chose milk gender and drink choice number who chose milk and number of boys number who chose milk and total students

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Problem 518

What dimensions must matrix $A$ have to map $\mathbb{R}^{6}$ to $\mathbb{R}^{7}$ using $T(\mathbf{x})=A \mathbf{x}$ ? A. 6 rows, 7 columns B. 6 rows, 6 columns C. 7 rows, 6 columns D. 7 rows, 7 columns

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Problem 519

Find all $\mathbf{x}$ in $\mathbb{R}^{4}$ such that $A \mathbf{x} = \mathbf{0}$ for the matrix $A=\begin{bmatrix} 1 & 2 & 7 & -1 \\ 1 & 0 & 3 & -4 \\ 0 & 1 & 2 & 3 \\ -1 & 5 & 7 & 4 \end{bmatrix}$ . Choose A, B, C, or D.

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Problem 520

Score I 、Fill in the blanks. (Questions 1 to 5 carry 2 marks each. 10 marks totally.)
1. Let $\vec{u}=(2,5,-3), \vec{v}=(-4,1,9)$ . Then $2 \vec{u}-3 \vec{v}=$ $\qquad$
2. The dot product of $\vec{u}=(1,-2,4)$ and $\vec{v}=(3,1,2)$ is $\qquad$ .
3. The trace of the matrix $A=\left(\begin{array}{ccc}4 & 1 & -2 \\ 2 & -3 & 6 \\ 7 & 3 & 0\end{array}\right)$ is $\qquad$ .
4. A square matrix $A$ is said to be singular if $\qquad$
5. The distance between the noints $\vec{\gamma}-1$

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Problem 521

7. Let $A, B$ and $C$ be $n \times n$ matrices. $I$ is an $n \times n$ matrix. The following statement is correct ( ). A. If $A B=A C$ and $A \neq 0$ , then $B=C$ . B. If $A^{2}=A$ , then $A=0$ or $A=I$ . C. If $A^{2}=0$ , then $A=0$ . D. If $A B=B A$ , then $(A+B)^{2}=A^{2}+2 A B+B^{2}$ .

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Problem 522

8. Let $A, B$ be invertible $3 \times 3$ matrices. The following conclusion is correct ( ). A. $(A+B)^{-1}=A^{-1}+B^{-1}$ B. $(A B)^{-1}=A^{-1} B^{-1}$ C. $(A B)^{t}=B^{t} A^{t}$ D. $|3 A|=3|A|$
9. The cofactor $C_{21}$ of matrix $\left(\begin{array}{ccc}1 & 2 & -3 \\ 5 & 0 & 6 \\ 7 & 1 & -4\end{array}\right)$ is $(\quad)$ . A. 5 B. -1 C. -5 D. 1
10. Let $A$ be an $n \times n$ matrix and $|A|=2$ . Then $\left||A| A^{t}\right|=(\quad)$ . A. $2^{n}$ B. $2^{n-1}$ C. $2^{n+1}$ D. 4 III. Solve the questions. (Questions 11 to 15 carry 10 marks each. 50 marks Score totally.)
11. Let $A=\left[\begin{array}{ccc}3 & 4 & -2 \\ 5 & -1 & 2\end{array}\right], \quad B=\left[\begin{array}{ccc}1 & -2 & 1 \\ 1 & -4 & 3\end{array}\right], \quad C=\left[\begin{array}{cc}5 & 2 \\ -2 & 1\end{array}\right]$ . Compute $2 A-3 B, C A$ .

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Problem 523

Find the standard matrix for the linear transformation $T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ that rotates points by $-\frac{5 \pi}{4}$ radians. $A=$

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Problem 524

Find the standard matrix of the linear transformation $T$ that reflects points first through $x_{2}=-x_{1}$ and then the $x_{2}$ -axis. $A=$ (Enter values for each matrix element.)

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Problem 525

How many rows and columns must matrix $A$ have to map $\mathbb{R}^{8}$ to $\mathbb{R}^{9}$ using $T(x)=A x$ ? A. 9 rows, 9 columns B. 9 rows, 8 columns C. 8 rows, 8 columns D. 8 rows, 9 columns

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Problem 526

Find all $\mathbf{x}$ in $\mathbb{R}^{4}$ such that $A \mathbf{x} = \mathbf{0}$ for the matrix $A = \begin{bmatrix} 1 & 4 & 16 & 8 \\ 1 & 0 & 4 & -4 \\ 0 & 1 & 3 & 4 \\ -2 & 0 & -8 & -4 \end{bmatrix}$ .

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Problem 527

Find the standard matrix of the linear transformation $T: \mathbb{R}^{3} \rightarrow \mathbb{R}^{2}$ given $T(\mathbf{e}_{1})=(1,9)$ , $T(\mathbf{e}_{2})=(-4,6)$ , $T(\mathbf{e}_{3})=(9,-8)$ . $A=\square$ (Type an integer or decimal for each matrix element.)

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Problem 528

Find the standard matrix for the linear transformation $T$ that rotates points in $\mathbb{R}^2$ by $-\frac{\pi}{2}$ radians. $A =$ (Enter exact values for each matrix element.)

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Problem 529

Determine the determinant $D=\left|\begin{array}{ccc}0 & 5 & 2 \\ 4 & -3 & 0 \\ 2 & 4 & 2\end{array}\right|$
Let $\vec{u}=(3,-1,2)$ and $\vec{v}=(4,1,1)$ . Normalize the vector $\vec{u}$ . Determine the cosines of the angles between $\vec{u}$ and

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Matrix

Problem 501

MATh140 Second Firstsem-2024-2025, (161745)(-4) mentieQuestion 8 of 18 A matrix that is both sympetric and upper triangular must be a diagonal matrix. True Falle

Problem 502

Question 16 of 18 Let AAA be 2×22 \times 22×2 matrix with det⁡(A)=−2\operatorname{det}(A)=-2det(A)=−2, then det⁡(4A−1)=\operatorname{det}\left(4 A^{-1}\right)=det(4A−1)= 8 - 2 2 1/81 / 81/8

Problem 503

Calculate nnn using the formula n=A⋅B×ACn = A \cdot B \times A Cn=A⋅B×AC and the determinant ∣3112−1−3∣\left| \begin{array}{ccc} 3 & 1 & 1 \\ 2 & -1 & -3 \end{array} \right|∣∣​32​1−1​1−3​∣∣​.

Problem 504

Problem 505

浙江科技大学考试试卷4. The state of plane stress at a point with respect to the xyx yxy-axes is shown in Figure. Determine the principal stresses and principal planes. Show the results on a sketch of an element aligned with the principal directions. (25 points）

Problem 506

If [371]⋅[536]=[x1]\left[\begin{array}{lll}3 & 7 & 1\end{array}\right] \cdot\left[\begin{array}{l}5 \\ 3 \\ 6\end{array}\right]=\left[x_{1}\right][3​7​1​]⋅⎣⎡​536​⎦⎤​=[x1​], what is the value of x1x_{1}x1​ ? If the matrix operation is not possible, write "none".

Problem 507

Given matrix AAA and vector b\mathbf{b}b, determine if b\mathbf{b}b is in the span of columns of AAA. How many vectors are in this span?

Problem 508

Given matrix AAA and vector bbb, check if bbb is in the span of columns of AAA. How many vectors are in the set?

Problem 509

Given matrix AAA and vector bbb, determine if bbb is in the span of columns of AAA. How many vectors are in this span?

Problem 510

Ms. Lowell's class has a decimal chart. Answer these: 5. What pattern do you see moving left to right? 6. How does the last square in each row differ? 7. What pattern do you observe moving down a column?

Problem 511

Fill in the missing values in the table using totals. If unknown + 67 = 99, then unknown = 32. Total students who play sports and an instrument = 35.

Problem 512

Temukan nilai eigen dan vektor eigen dan matriks A -3 3 3-5 3 6-64

Problem 513

1. Temukan nilai eigen dan vektor eigen dari matriks A=[1−333−536−64]A=\left[\begin{array}{ccc}1 & -3 & 3 \\ 3 & -5 & 3 \\ 6 & -6 & 4\end{array}\right]A=⎣⎡​136​−3−5−6​334​⎦⎤​

Problem 514

Problem 515

Problem 516

Problem 517

Problem 518

What dimensions must matrix AAA have to map R6\mathbb{R}^{6}R6 to R7\mathbb{R}^{7}R7 using T(x)=AxT(\mathbf{x})=A \mathbf{x}T(x)=Ax? A. 6 rows, 7 columns B. 6 rows, 6 columns C. 7 rows, 6 columns D. 7 rows, 7 columns

Problem 519

Problem 520

Problem 521

Problem 522

Problem 523

Find the standard matrix for the linear transformation T:R2→R2T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}T:R2→R2 that rotates points by −5π4-\frac{5 \pi}{4}−45π​ radians. A=A=A=

Problem 524

Find the standard matrix of the linear transformation TTT that reflects points first through x2=−x1x_{2}=-x_{1}x2​=−x1​ and then the x2x_{2}x2​-axis. A=A=A= (Enter values for each matrix element.)

Problem 525

How many rows and columns must matrix AAA have to map R8\mathbb{R}^{8}R8 to R9\mathbb{R}^{9}R9 using T(x)=AxT(x)=A xT(x)=Ax? A. 9 rows, 9 columns B. 9 rows, 8 columns C. 8 rows, 8 columns D. 8 rows, 9 columns

Problem 526

Problem 527

Problem 528

Find the standard matrix for the linear transformation TTT that rotates points in R2\mathbb{R}^2R2 by −π2-\frac{\pi}{2}−2π​ radians. A= A = A= (Enter exact values for each matrix element.)

Problem 529

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MATh140 Second Firstsem-2024-2025, (161745)(-4) mentie
Question 8 of 18 A matrix that is both sympetric and upper triangular must be a diagonal matrix. True Falle

Question 16 of 18 Let $A$ be $2 \times 2$ matrix with $\operatorname{det}(A)=-2$ , then $\operatorname{det}\left(4 A^{-1}\right)=$ 8 - 2 2 $1 / 8$

Calculate $n$ using the formula $n = A \cdot B \times A C$ and the determinant $\left| \begin{array}{ccc} 3 & 1 & 1 \\ 2 & -1 & -3 \end{array} \right|$ .

浙江科技大学考试试卷
4. The state of plane stress at a point with respect to the $x y$ -axes is shown in Figure. Determine the principal stresses and principal planes. Show the results on a sketch of an element aligned with the principal directions. (25 points）

If $\left[\begin{array}{lll}3 & 7 & 1\end{array}\right] \cdot\left[\begin{array}{l}5 \\ 3 \\ 6\end{array}\right]=\left[x_{1}\right]$ , what is the value of $x_{1}$ ? If the matrix operation is not possible, write "none".

Given matrix $A$ and vector $\mathbf{b}$ , determine if $\mathbf{b}$ is in the span of columns of $A$ . How many vectors are in this span?

Given matrix $A$ and vector $b$ , check if $b$ is in the span of columns of $A$ . How many vectors are in the set?

Given matrix $A$ and vector $b$ , determine if $b$ is in the span of columns of $A$ . How many vectors are in this span?

Ms. Lowell's class has a decimal chart. Answer these:
5. What pattern do you see moving left to right?
6. How does the last square in each row differ?
7. What pattern do you observe moving down a column?

1. Temukan nilai eigen dan vektor eigen dari matriks $A=\left[\begin{array}{ccc}1 & -3 & 3 \\ 3 & -5 & 3 \\ 6 & -6 & 4\end{array}\right]$

What dimensions must matrix $A$ have to map $\mathbb{R}^{6}$ to $\mathbb{R}^{7}$ using $T(\mathbf{x})=A \mathbf{x}$ ? A. 6 rows, 7 columns B. 6 rows, 6 columns C. 7 rows, 6 columns D. 7 rows, 7 columns

Find the standard matrix for the linear transformation $T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ that rotates points by $-\frac{5 \pi}{4}$ radians. $A=$

Find the standard matrix of the linear transformation $T$ that reflects points first through $x_{2}=-x_{1}$ and then the $x_{2}$ -axis. $A=$ (Enter values for each matrix element.)

How many rows and columns must matrix $A$ have to map $\mathbb{R}^{8}$ to $\mathbb{R}^{9}$ using $T(x)=A x$ ? A. 9 rows, 9 columns B. 9 rows, 8 columns C. 8 rows, 8 columns D. 8 rows, 9 columns

Find the standard matrix for the linear transformation $T$ that rotates points in $\mathbb{R}^2$ by $-\frac{\pi}{2}$ radians. $A =$ (Enter exact values for each matrix element.)