Matrices

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See

Exercises

  1. If the matrix is invertible, determine the inverse of $M = \begin{pmatrix} 0 & 5 & 1 \ 1 & 3 & 0 \ 1 & 0 & 2 \end{pmatrix}$

  2. If the matrix is invertible, determine the inverse of $M = \begin{pmatrix} 0 & 1 & 2 \ 0 & 1 & 1 \ 1 & 0 & 0 \end{pmatrix}$

  3. If the matrix is invertible, determine the inverse of $M = \begin{pmatrix} 1 & 1 & 2 \ 1 & 1 & 1 \ 1 & 0 & 0 \end{pmatrix}$

  4. Determine the inverse of $\begin{pmatrix} 1 & 0 & 0 \ 0 & -2 & 0 \ 0 & 0 & 3 \end{pmatrix}$

  5. If the matrix is invertible, determine the inverse of $M = \begin{pmatrix} 0 & 1 & 1 \ 1 & 0 & 0 \ 0 & 1 & 2 \end{pmatrix}$

  6. Determine the inverse of $\begin{pmatrix} 1 & 0 & 0 \ 0 & -2 & 0 \ 0 & 0 & 1 \end{pmatrix}$

  7. Determine the inverse of $\begin{pmatrix} 4 & 0 & 0 \ 0 & -2 & 0 \ 0 & 0 & 1 \end{pmatrix}$

  8. For the matrix $A = \begin{pmatrix} 0 & 1 & 1/2 \ -5 & \sqrt{3} & 1 \end{pmatrix}$, find:
    • $a_{21}$, $a_{12}$, $a_{23}$
    • $A(2)$ (the second row)
    • $A^{(2)}$ (the second column)
  9. Calculate $A + B$ given the matrices:
    • $A = \begin{pmatrix} 1 & -2 \ \pi & 1 \end{pmatrix}$
    • $B = \begin{pmatrix} -1 & 1 \ 1 & 1/2 \end{pmatrix}$