Consider the matrices \( A \) and \( B \) given below. How many rows and how many columns does the product \( C = A B \) have?
\( A = \left[ \begin{array} { l l } { 0 } & { 1 } \\ { 1 } & { 0 } \\ { 0 } & { k } \end{array} \right] , B = \left[ \begin{array} { c c c c } { 30 } & { 0 } & { 5 } & { 0 } \\ { 0 } & { 100 } & { 0 } & { 71 } \end{array} \right]\)
Number of rows:
Number of columns:
The entries of the matrix \( C = A B \) are denoted \( c _ { i j } \) , where \( c _ { i j } \) denotes the entry in the \(i^{th} \) and the \(j^{th} \) column. Insert below the values of the requested entries.
\(c _ { 13 } = c _ { 11 } = c _ { 21 } = \)
\( c _ { 23 } = c _ { 31 } = c _ { 33 } = \)
Given that \( c _ { 32 } = 79 \) , find the value of \( k \) and hence find the sum of the entries of \( C \) .
\( k = \)
The sum of the entries of \( C \) is
Enter your answer as a fraction.