Tutorial Week 6
Inverting Matrices
Q1: Find the inverse of \(\begin{bmatrix} 3 & 2 & 2 \\ 1 & 5 & 3 \\ 0 & 1 & 0 \end{bmatrix}\).
Solving System of Equations with Inverse Matrices
Q2: Solve the system of equations \(\begin{cases} 2x + y = 1 \\ x - y = 8 \end{cases}\) using matrix inverses.
Equations with Inverse Matrices
Q3: Find the matrix \(A\) if \(((2A + I)^{-1})^T + \begin{bmatrix} 1 & 0 \\ 1 & 0 \end{bmatrix} ^T = \begin{bmatrix} 1 & 3 \\ 1 & 2 \end{bmatrix}\).
Determinants
Q4: Compute the determinant of \(\begin{bmatrix} 3 & 1 & 2 \\ -2 & 0 & 5 \\ 1 & 1 & 5 \end{bmatrix}\).
Q5: If A and B are 3 by 3 matrices, \(\text{det}(A) = 7\) and \(\text{det}(B) = 2\), find \(\text{det}(3A^TB^{-1}B^T2A)\).
