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ad-work [718]
3 years ago
9

Compute the product AB by the definition of the product of​ matrices, where A and A are computed​ separately, and by the​ row-co

lumn 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.
Mathematics
1 answer:
chubhunter [2.5K]3 years ago
5 0

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

Step-by-step 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)}

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