QUESTION IMAGE
Question
the inverse of a matrix in exercises 5, 6, 7, 8, 9, 10, 11, and 12, show that ( b ) is the inverse
- ( a = \begin{bmatrix} 2 & 1 \\ 5 & 3 end{bmatrix}, quad b = \begin{bmatrix} 3 & -1 \\ -5 & 2 end{bmatrix} )
- ( a = \begin{bmatrix} 1 & -1 \\ -1 & 2 end{bmatrix}, quad b = \begin{bmatrix} 2 & 1 \\ 1 & 1 end{bmatrix} )
Problem 5
To show that \( B \) is the inverse of \( A \), we need to verify that \( AB = I \) and \( BA = I \), where \( I \) is the identity matrix.
Step 1: Calculate \( AB \)
Given \( A =
\) and \( B =
\)
Step 2: Calculate \( BA \)
Since \( AB = I \) and \( BA = I \), \( B \) is the inverse of \( A \).
Problem 6
To show that \( B \) is the inverse of \( A \), we need to verify that \( AB = I \) and \( BA = I \), where \( I \) is the identity matrix.
Step 1: Calculate \( AB \)
Given \( A =
\) and \( B =
\)
Step 2: Calculate \( BA \)
Since \( AB = I \) and \( BA = I \), \( B \) is the inverse of \( A \).
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Problem 5
To show that \( B \) is the inverse of \( A \), we need to verify that \( AB = I \) and \( BA = I \), where \( I \) is the identity matrix.
Step 1: Calculate \( AB \)
Given \( A =
\) and \( B =
\)
Step 2: Calculate \( BA \)
Since \( AB = I \) and \( BA = I \), \( B \) is the inverse of \( A \).
Problem 6
To show that \( B \) is the inverse of \( A \), we need to verify that \( AB = I \) and \( BA = I \), where \( I \) is the identity matrix.
Step 1: Calculate \( AB \)
Given \( A =
\) and \( B =
\)
Step 2: Calculate \( BA \)
Since \( AB = I \) and \( BA = I \), \( B \) is the inverse of \( A \).