Studdy AI Logo
Math
Arithmetic
Fractions and Decimals
Measurement
Geometry
Word Problems
Algebra
Calculus
Statistics
Probability
Number Theory
Discrete Mathematics
Linear Algebra
Differential Equations
Trigonometry
Finance
Solved on Nov 16, 2023

Perform matrix operations on AA, BB, CC, and DD matrices, such as B+DB+D and B−AB-A.

STEP 1

Assumptions1. The matrices are given as followsA=[7194−6−1−]B=[−129−5−116]C=[113−4−87]D=[−1401−5109]A=\left[\begin{array}{cc} 7 &19 \\ 4 & -6 \\ -1 & -\end{array}\right] \quad B=\left[\begin{array}{cc} -12 &9 \\ -5 & -1 \\ 16 &\end{array}\right] \quad C=\left[\begin{array}{ccc} 1 &13 & -4 \\ & -8 &7\end{array}\right] \quad D=\left[\begin{array}{cc} -14 &0 \\ 1 & -5 \\ 10 &9\end{array}\right] . We are asked to perform the operations B+B+ and B−AB-A.
3. The addition and subtraction of matrices is only possible if the matrices have the same dimensions.

STEP 2

First, we need to check if the matrices BB and $$ have the same dimensions, as we are asked to perform the operation $B+$.
Matrix BB is a ×2 \times2 matrix and matrix $$ is also a $ \times2$ matrix. Therefore, the addition is possible.

STEP 3

Now, perform the addition operation B+B+. The addition of two matrices is done element by element.
B+=[−12+(−14)9+0−5+1−1+(−5)16+102+9]B+ = \left[\begin{array}{cc} -12+(-14) &9+0 \\ -5+1 & -1+(-5) \\ 16+10 &2+9\end{array}\right]

STEP 4

Calculate the elements of the resulting matrix.
B+=[−269−4−62611]B+ = \left[\begin{array}{cc} -26 &9 \\ -4 & -6 \\ 26 &11\end{array}\right]

STEP 5

Next, we need to check if the matrices BB and AA have the same dimensions, as we are asked to perform the operation B−AB-A.
Matrix BB is a 3×23 \times2 matrix and matrix AA is also a 3×23 \times2 matrix. Therefore, the subtraction is possible.

STEP 6

Now, perform the subtraction operation B−AB-A. The subtraction of two matrices is done element by element.
B−A=[−12−9−19−5−4−1−(−6)16−(−1)2−(−2)]B-A = \left[\begin{array}{cc} -12- &9-19 \\ -5-4 & -1-(-6) \\ 16-(-1) &2-(-2) \end{array}\right]

STEP 7

Calculate the elements of the resulting matrix.
B−A=[−19−10−95174]B-A = \left[\begin{array}{cc} -19 & -10 \\ -9 &5 \\ 17 &4\end{array}\right]So, the results of the operations areB+=[−269−4−62611]B+ = \left[\begin{array}{cc} -26 &9 \\ -4 & -6 \\ 26 &11\end{array}\right]andB−A=[−19−10−95174]B-A = \left[\begin{array}{cc} -19 & -10 \\ -9 &5 \\ 17 &4\end{array}\right]

Was this helpful?
banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ContactInfluencer programPolicyTerms
TwitterInstagramFacebookTikTokDiscord