Solved on Dec 15, 2023

Find $C-A+B$ and simplify, if possible. Give exact answers in fraction form, if necessary. Select "Undefined" if applicable.

STEP 1

Assumptions
1. Matrices $A$ , $B$ , and $C$ are given.
2. We need to find the result of the matrix operation $C - A + B$ .
3. The operation must be performed by subtracting and adding corresponding elements of the matrices.

STEP 2

First, we need to subtract matrix $A$ from matrix $C$ . We do this by subtracting each corresponding element in matrix $A$ from matrix $C$ .
$C - A = \left[\begin{array}{cc} 14 & 2 \\ 3 & -\frac{1}{3} \\ 2 & 3 \end{array}\right] - \left[\begin{array}{cc} 6 & -2 \\ 3 & \frac{1}{2} \\ 2 & \sqrt{2} \end{array}\right]$

STEP 3

Perform the subtraction for each element.
$C - A = \left[\begin{array}{cc} 14 - 6 & 2 - (-2) \\ 3 - 3 & -\frac{1}{3} - \frac{1}{2} \\ 2 - 2 & 3 - \sqrt{2} \end{array}\right]$

STEP 4

Simplify the subtraction for each element.
$C - A = \left[\begin{array}{cc} 8 & 4 \\ 0 & -\frac{1}{3} - \frac{1}{2} \\ 0 & 3 - \sqrt{2} \end{array}\right]$

STEP 5

Combine the fractions in the second element of the second row.
$-\frac{1}{3} - \frac{1}{2} = -\frac{2}{6} - \frac{3}{6} = -\frac{5}{6}$

STEP 6

Now we have the result of $C - A$ .
$C - A = \left[\begin{array}{cc} 8 & 4 \\ 0 & -\frac{5}{6} \\ 0 & 3 - \sqrt{2} \end{array}\right]$

STEP 7

Next, we need to add matrix $B$ to the result of $C - A$ . We do this by adding each corresponding element in matrix $B$ to the result of $C - A$ .
$C - A + B = \left[\begin{array}{cc} 8 & 4 \\ 0 & -\frac{5}{6} \\ 0 & 3 - \sqrt{2} \end{array}\right] + \left[\begin{array}{cc} -8 & 1 \\ 7.4 & 6 \\ \frac{1}{4} & \sqrt{8} \end{array}\right]$

STEP 8

Perform the addition for each element.
$C - A + B = \left[\begin{array}{cc} 8 + (-8) & 4 + 1 \\ 0 + 7.4 & -\frac{5}{6} + 6 \\ 0 + \frac{1}{4} & (3 - \sqrt{2}) + \sqrt{8} \end{array}\right]$

STEP 9

Simplify the addition for each element.
$C - A + B = \left[\begin{array}{cc} 0 & 5 \\ 7.4 & -\frac{5}{6} + \frac{36}{6} \\ \frac{1}{4} & 3 - \sqrt{2} + \sqrt{8} \end{array}\right]$

STEP 10

Combine the fractions in the second element of the second row.
$-\frac{5}{6} + \frac{36}{6} = \frac{31}{6}$

STEP 11

Simplify the square root in the second element of the third row.
$\sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2}$

STEP 12

Now we have the result of $C - A + B$ .
$C - A + B = \left[\begin{array}{cc} 0 & 5 \\ 7.4 & \frac{31}{6} \\ \frac{1}{4} & 3 - \sqrt{2} + 2\sqrt{2} \end{array}\right]$

STEP 13

Simplify the second element of the third row.
$3 - \sqrt{2} + 2\sqrt{2} = 3 + \sqrt{2}$

STEP 14

Now we have the final simplified form of $C - A + B$ .
$C - A + B = \left[\begin{array}{cc} 0 & 5 \\ 7.4 & \frac{31}{6} \\ \frac{1}{4} & 3 + \sqrt{2} \end{array}\right]$
This is the simplified result of the matrix operation $C - A + B$ .

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Find $C-A+B$ and simplify, if possible. Give exact answers in fraction form, if necessary. Select "Undefined" if applicable.

STEP 1

Assumptions
1. Matrices $A$ , $B$ , and $C$ are given.
2. We need to find the result of the matrix operation $C - A + B$ .
3. The operation must be performed by subtracting and adding corresponding elements of the matrices.

STEP 2

STEP 3

Perform the subtraction for each element.
$C - A = \left[\begin{array}{cc} 14 - 6 & 2 - (-2) \\ 3 - 3 & -\frac{1}{3} - \frac{1}{2} \\ 2 - 2 & 3 - \sqrt{2} \end{array}\right]$

STEP 4

Simplify the subtraction for each element.
$C - A = \left[\begin{array}{cc} 8 & 4 \\ 0 & -\frac{1}{3} - \frac{1}{2} \\ 0 & 3 - \sqrt{2} \end{array}\right]$

STEP 5

Combine the fractions in the second element of the second row.
$-\frac{1}{3} - \frac{1}{2} = -\frac{2}{6} - \frac{3}{6} = -\frac{5}{6}$

STEP 6

Now we have the result of $C - A$ .
$C - A = \left[\begin{array}{cc} 8 & 4 \\ 0 & -\frac{5}{6} \\ 0 & 3 - \sqrt{2} \end{array}\right]$

STEP 7

STEP 8

Perform the addition for each element.
$C - A + B = \left[\begin{array}{cc} 8 + (-8) & 4 + 1 \\ 0 + 7.4 & -\frac{5}{6} + 6 \\ 0 + \frac{1}{4} & (3 - \sqrt{2}) + \sqrt{8} \end{array}\right]$

STEP 9

Simplify the addition for each element.
$C - A + B = \left[\begin{array}{cc} 0 & 5 \\ 7.4 & -\frac{5}{6} + \frac{36}{6} \\ \frac{1}{4} & 3 - \sqrt{2} + \sqrt{8} \end{array}\right]$

STEP 10

Combine the fractions in the second element of the second row.
$-\frac{5}{6} + \frac{36}{6} = \frac{31}{6}$

STEP 11

Simplify the square root in the second element of the third row.
$\sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2}$

STEP 12

Now we have the result of $C - A + B$ .
$C - A + B = \left[\begin{array}{cc} 0 & 5 \\ 7.4 & \frac{31}{6} \\ \frac{1}{4} & 3 - \sqrt{2} + 2\sqrt{2} \end{array}\right]$

STEP 13

Simplify the second element of the third row.
$3 - \sqrt{2} + 2\sqrt{2} = 3 + \sqrt{2}$

STEP 14

Now we have the final simplified form of $C - A + B$ .
$C - A + B = \left[\begin{array}{cc} 0 & 5 \\ 7.4 & \frac{31}{6} \\ \frac{1}{4} & 3 + \sqrt{2} \end{array}\right]$
This is the simplified result of the matrix operation $C - A + B$ .

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Find C−A+BC-A+BC−A+B and simplify, if possible. Give exact answers in fraction form, if necessary. Select "Undefined" if applicable.

STEP 1

Assumptions1. Matrices AAA, BBB, and CCC are given.2. We need to find the result of the matrix operation C−A+BC - A + BC−A+B.3. The operation must be performed by subtracting and adding corresponding elements of the matrices.

STEP 2

STEP 3

STEP 4

Simplify the subtraction for each element.C−A=[840−13−1203−2]C - A = \left[\begin{array}{cc} 8 & 4 \\ 0 & -\frac{1}{3} - \frac{1}{2} \\ 0 & 3 - \sqrt{2} \end{array}\right]C−A=⎣⎡​800​4−31​−21​3−2​​⎦⎤​

STEP 5

Combine the fractions in the second element of the second row.−13−12=−26−36=−56-\frac{1}{3} - \frac{1}{2} = -\frac{2}{6} - \frac{3}{6} = -\frac{5}{6}−31​−21​=−62​−63​=−65​

STEP 6

Now we have the result of C−AC - AC−A.C−A=[840−5603−2]C - A = \left[\begin{array}{cc} 8 & 4 \\ 0 & -\frac{5}{6} \\ 0 & 3 - \sqrt{2} \end{array}\right]C−A=⎣⎡​800​4−65​3−2​​⎦⎤​

STEP 7

STEP 8

STEP 9

Simplify the addition for each element.C−A+B=[057.4−56+366143−2+8]C - A + B = \left[\begin{array}{cc} 0 & 5 \\ 7.4 & -\frac{5}{6} + \frac{36}{6} \\ \frac{1}{4} & 3 - \sqrt{2} + \sqrt{8} \end{array}\right]C−A+B=⎣⎡​07.441​​5−65​+636​3−2​+8​​⎦⎤​

STEP 10

Combine the fractions in the second element of the second row.−56+366=316-\frac{5}{6} + \frac{36}{6} = \frac{31}{6}−65​+636​=631​

STEP 11

Simplify the square root in the second element of the third row.8=4⋅2=22\sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2}8​=4⋅2​=22​

STEP 12

Now we have the result of C−A+BC - A + BC−A+B.C−A+B=[057.4316143−2+22]C - A + B = \left[\begin{array}{cc} 0 & 5 \\ 7.4 & \frac{31}{6} \\ \frac{1}{4} & 3 - \sqrt{2} + 2\sqrt{2} \end{array}\right]C−A+B=⎣⎡​07.441​​5631​3−2​+22​​⎦⎤​

STEP 13

Simplify the second element of the third row.3−2+22=3+23 - \sqrt{2} + 2\sqrt{2} = 3 + \sqrt{2}3−2​+22​=3+2​

STEP 14

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Find $C-A+B$ and simplify, if possible. Give exact answers in fraction form, if necessary. Select "Undefined" if applicable.

Assumptions
1. Matrices $A$ , $B$ , and $C$ are given.
2. We need to find the result of the matrix operation $C - A + B$ .
3. The operation must be performed by subtracting and adding corresponding elements of the matrices.

Simplify the subtraction for each element.
$C - A = \left[\begin{array}{cc} 8 & 4 \\ 0 & -\frac{1}{3} - \frac{1}{2} \\ 0 & 3 - \sqrt{2} \end{array}\right]$

Combine the fractions in the second element of the second row.
$-\frac{1}{3} - \frac{1}{2} = -\frac{2}{6} - \frac{3}{6} = -\frac{5}{6}$

Now we have the result of $C - A$ .
$C - A = \left[\begin{array}{cc} 8 & 4 \\ 0 & -\frac{5}{6} \\ 0 & 3 - \sqrt{2} \end{array}\right]$

Simplify the addition for each element.
$C - A + B = \left[\begin{array}{cc} 0 & 5 \\ 7.4 & -\frac{5}{6} + \frac{36}{6} \\ \frac{1}{4} & 3 - \sqrt{2} + \sqrt{8} \end{array}\right]$

Combine the fractions in the second element of the second row.
$-\frac{5}{6} + \frac{36}{6} = \frac{31}{6}$

Simplify the square root in the second element of the third row.
$\sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2}$

Now we have the result of $C - A + B$ .
$C - A + B = \left[\begin{array}{cc} 0 & 5 \\ 7.4 & \frac{31}{6} \\ \frac{1}{4} & 3 - \sqrt{2} + 2\sqrt{2} \end{array}\right]$

Simplify the second element of the third row.
$3 - \sqrt{2} + 2\sqrt{2} = 3 + \sqrt{2}$