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Algebra
Question

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

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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