Question

Compute the product AB by the definition of the product of​ matrices, where A and A are computed​ separately, and by the​ row-column rule for computing AB. A ​, B Set up the product A​, where is the first column of B. A nothing nothing ​(Use one answer box for A and use the other answer box for ​.) Calculate A​, where is the first column of B. A nothing ​(Type an integer or decimal for each matrix​ element.) Set up the product A​, where is the second column of B. A nothing nothing ​(Use one answer box for A and use the other answer box for ​.) Calculate A​, where is the second column of B.

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

First question

`Ab_1 = \left[\begin{array}{ccc}{-1}&{3}\\ 1 &4 \\5 &8\end{array}\right]\left[\begin{array}{ccc}5\\-2\\\end{array}\right]`

Second question

`Ab_1 = \left[\begin{array}{ccc}{-1}&{3}\\ 1 &4 \\5 &8\end{array}\right]\left[\begin{array}{ccc}5\\-2\\\end{array}\right] = \left[\begin{array}{ccc}{(-1 * 5 )+ (3* -2)}\\{(1 * 5)+ (4 * -2)}\\{(5 * 5) + (8*-2)}\end{array}\right] = \left[\begin{array}{ccc}{-11}\\{-3}\\{29}\end{array}\right]`

Third question

`Ab_1 = \left[\begin{array}{ccc}{-1}&{3}\\ 1 &4 \\5 &8\end{array}\right]\left[\begin{array}{ccc}-3\\4\\\end{array}\right]`

Fourth question

`Ab_1 = \left[\begin{array}{ccc}{-1}&{3}\\ 1 &4 \\5 &8\end{array}\right]\left[\begin{array}{ccc}-3\\4\\\end{array}\right] = \left[\begin{array}{ccc}{(-1 * -3 )+ (3* 4)}\\{(1 * -3)+ (4 * 4)}\\{(5 * -3) + (8*4)}\end{array}\right] = \left[\begin{array}{ccc}{15}\\{13}\\{-23}\end{array}\right]`

Fifth question

The correct option is A

Explanation:

From the question we are told that

The matrix A is
`A = \left[\begin{array}{ccc}{-1}&{3}\\ 1 &4 \\5 &8\end{array}\right]`

The matrix B is
`B = \left[\begin{array}{ccc}5&{-3}\\{-2}&4\end{array}\right]`

The first question is to set up the product
`Ab_1` , where
`b_1` is the first column of matrix B, this shown as

`Ab_1 = \left[\begin{array}{ccc}{-1}&{3}\\ 1 &4 \\5 &8\end{array}\right]\left[\begin{array}{ccc}5\\-2\\\end{array}\right]`

The second question is to calculate
`Ab_1` , this is evaluated as

`Ab_1 = \left[\begin{array}{ccc}{-1}&{3}\\ 1 &4 \\5 &8\end{array}\right]\left[\begin{array}{ccc}5\\-2\\\end{array}\right] = \left[\begin{array}{ccc}{(-1 * 5 )+ (3* -2)}\\{(1 * 5)+ (4 * -2)}\\{(5 * 5) + (8*-2)}\end{array}\right] = \left[\begin{array}{ccc}{-11}\\{-3}\\{29}\end{array}\right]`

The third question is to set up the product
`Ab_2` , where
`b_2` is the second column of matrix B, this shown as

`Ab_1 = \left[\begin{array}{ccc}{-1}&{3}\\ 1 &4 \\5 &8\end{array}\right]\left[\begin{array}{ccc}-3\\4\\\end{array}\right]`

The fourth question is to calculate
`Ab_2` , this is evaluated as

`Ab_1 = \left[\begin{array}{ccc}{-1}&{3}\\ 1 &4 \\5 &8\end{array}\right]\left[\begin{array}{ccc}-3\\4\\\end{array}\right] = \left[\begin{array}{ccc}{(-1 * -3 )+ (3* 4)}\\{(1 * -3)+ (4 * 4)}\\{(5 * -3) + (8*4)}\end{array}\right] = \left[\begin{array}{ccc}{15}\\{13}\\{-23}\end{array}\right]`

The fifth question is to determine the numerical expression for the first entry in the first column of AB using the row-column rule and from the calculation of
`Ab_1` we see that it is

`{(-1 * 5 )+ (3* -2)}`