Please help! Correct answer only, please! Consider the matrix shown below: Find the inverse of the matrix A: (i.e Find A^-1).
1 answer:
Answer: a)
<u>Step-by-step explanation:</u>
Matrix multiplication is the sum of Row 1 (of first matrix) x Column 1 (of second matrix) ...repeat for each row.
Transpose means to switch the rows to columns.
![A=\left[\begin{array}{cc}5&2\\3&-1\end{array}\right] \qquad \times \qquad A^T=\left[\begin{array}{cc}5&3\\2&-1\end{array}\right] \\\\\\= \left[\begin{array}{cc}5(5)+2(2)&5(3)+2(-1)\\3(5)+(-1)(2)&3(3)+(-1)(-1)\end{array}\right] \\\\\\= \left[\begin{array}{cc}29&13\\13&10\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%262%5C%5C3%26-1%5Cend%7Barray%7D%5Cright%5D%20%5Cqquad%20%5Ctimes%20%5Cqquad%20A%5ET%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%263%5C%5C2%26-1%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5C%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%285%29%2B2%282%29%265%283%29%2B2%28-1%29%5C%5C3%285%29%2B%28-1%29%282%29%263%283%29%2B%28-1%29%28-1%29%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5C%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D29%2613%5C%5C13%2610%5Cend%7Barray%7D%5Cright%5D)
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