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.

[tex]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][/tex]

Third question

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

Fourth question

[tex]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][/tex]

Fifth question

The correct option is A

Step-by-step explanation:

From the question we are told that

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

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

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

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

The second question is to calculate [tex]Ab_1[/tex] , this is evaluated as

[tex]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][/tex]

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

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

The fourth question is to calculate [tex]Ab_2[/tex] , this is evaluated as

[tex]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][/tex]

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 [tex]Ab_1[/tex] we see that it is

[tex]{(-1 * 5 )+ (3* -2)}[/tex]