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Algebra
Question

Consider the matrices \( A \) and \( B \) given be...

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. 

Answer

rows: 3

columns: 4

\(c_{13}= 0,c_{11}= 0,c_{21}= 30\\c_{23}= 5,c_{31}= 0,c_{33}= 0\\c_{32}= 100k= 79\Rightarrow k= 0.79\)

 

sum=341.09

Solution
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