Preview Activity2.2.1Matrix operations

  1. Compute the scalar multiple

    \begin{equation*} -3\left[ \begin{array}{rrr} 3 \amp 1 \amp 0 \\ -4 \amp 3 \amp -1 \\ \end{array} \right] \text{.} \end{equation*}
  2. Suppose that \(A\) and \(B\) are two matrices. What do we need to know about their dimensions before we can form the sum \(A+B\text{?}\)

  3. Find the sum

    \begin{equation*} \left[ \begin{array}{rr} 0 \amp -3 \\ 1 \amp -2 \\ 3 \amp 4 \\ \end{array} \right] + \left[ \begin{array}{rrr} 4 \amp -1 \\ -2 \amp 2 \\ 1 \amp 1 \\ \end{array} \right] \text{.} \end{equation*}
  4. The matrix \(I_n\text{,}\) which we call the identity matrix is the \(n\times n\) matrix whose entries are zero except for the diagonal entries, which are 1. For instance,

    \begin{equation*} I_3 = \left[ \begin{array}{rrr} 1 \amp 0 \amp 0 \\ 0 \amp 1 \amp 0 \\ 0 \amp 0 \amp 1 \\ \end{array} \right] \text{.} \end{equation*}

    If we can form the sum \(A+I_n\text{,}\) what must be true about the matrix \(A\text{?}\)

  5. Find the matrix \(A - 2I_3\) where

    \begin{equation*} A = \left[ \begin{array}{rrr} 1 \amp 2 \amp -2 \\ 2 \amp -3 \amp 3 \\ -2 \amp 3 \amp 4 \\ \end{array} \right] \text{.} \end{equation*}
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