If A is the 2 × 2 matrix given by a b A = c d and if ad – bc # 0, the inverse is given by 1 d -b A-1 = ad – bc -C a Use the formula above to find the inverse of the 2 x 2 matrix (if it exists). (If an answer does not exist, enter DNE in any single blank.) 6 -3 4 -2
If A is the 2 × 2 matrix given by a b A = c d and if ad – bc # 0, the inverse is given by 1 d -b A-1 = ad – bc -C a Use the formula above to find the inverse of the 2 x 2 matrix (if it exists). (If an answer does not exist, enter DNE in any single blank.) 6 -3 4 -2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![If \( A \) is the 2 x 2 matrix given by
\[ A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \]
and if \( ad - bc \neq 0 \), the inverse is given by
\[ A^{-1} = \frac{1}{ad-bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}. \]
Use the formula above to find the inverse of the 2 x 2 matrix (if it exists). (If an answer does not exist, enter DNE in any single blank.)
Matrix provided:
\[
\begin{bmatrix} 6 & -3 \\ 4 & -2 \end{bmatrix}
\]
There are blank space holders in the form of a 2 x 2 matrix, signifying where the solution should be input. Green arrows point to the spaces, indicating where each component of the inverse calculation should go.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8669c346-3c1c-4fba-9bd7-ca273b01942a%2Fe58245a8-098d-47e6-a8c0-60b98b95bbb1%2Fkp79p6r_processed.png&w=3840&q=75)
Transcribed Image Text:If \( A \) is the 2 x 2 matrix given by
\[ A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \]
and if \( ad - bc \neq 0 \), the inverse is given by
\[ A^{-1} = \frac{1}{ad-bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}. \]
Use the formula above to find the inverse of the 2 x 2 matrix (if it exists). (If an answer does not exist, enter DNE in any single blank.)
Matrix provided:
\[
\begin{bmatrix} 6 & -3 \\ 4 & -2 \end{bmatrix}
\]
There are blank space holders in the form of a 2 x 2 matrix, signifying where the solution should be input. Green arrows point to the spaces, indicating where each component of the inverse calculation should go.
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