The Inverse of a Matrix

  1. Find the inverse of the matrix.    solution

    2. \( A=\left[\begin{array}{rr}{2} & {1} \\
    {-1} & {2}
    \end{array}\right]\)


  2. Find the inverse of the matrix.   solution

    3. \( A=\left[\begin{array}{rrr}{-2} & {-4} & {-3}\\
    {1} & {2} & {4} \\
    {0} & {1} & {5}
    \end{array}\right]\)


  3. (a) Suppose \((B-C)A=0,\) where B and C are \( m \times n \) matrices and \(A\) is invertible. Show that \( B=C. \)
    (b) Suppose \(A\) is invertible. Then show that \( A^{-1}=(A^{T}A)^{-1}A^T. \)

    4. solution