Question

PLZ HELP 20 PTS

Match each value to the correct entry in matrix AB.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The matrix AB is:

$AB=\left[\begin{array}{ccc}50&44&-43\\31&16&7\\37&119&-94\end{array}\right]$

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This question is solved using multiplication of matrices.

To do this, we multiply the lines of the first matrix by the columns of the second.

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In this question:

The first matrix is:

$A =\left[\begin{array}{ccc}5&7&2\\4&-1&3\\6&8&-5\end{array}\right]$

The second matrix is:

$B = \left[\begin{array}{ccc}6&11&-4\\2&1&-5\\3&-9&6\end{array}\right]$

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First line:

• The first element is the multiplication of the first line of A by the first column of B. So:
• $AB_{1,1} = 5\times6  + 7\times2 + 2\times3 = 50$
• The second element is the multiplication of the first line of A by the second column of B. So:
• $AB_{1,2} = 5\times11 + 7\times1 + 2\times -9 = 44$
• The third element is the multiplication of the first line of A by the third column of B. So:
• $AB_{1,3} = 5\times -4 + 7\times-5 + 2\times6 = -43$

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Second line:

Second line of A by each column of B, so:

$A_{2,1} = 4\times6 - 1\times 2 + 3\times3 = 31$

$A_{2,2} = 4\times11 - 1\times 1 + 3\times (-9) = 16$

$A_{2,3} = 4\times(-4) - 1\times (-5) + 3\times 6 = 7$

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Third line:

Third line of A by each column of B, so:

$A_{3,1} = 6\times6 + 8\times 2 - 5\times3 = 37$

$A_{3,2} = 6\times11 + 8\times 1 - 5\times (-9) = 119$

$A_{3,3} = 6\times(-4) + 8\times (-5) - 5\times 6 = -94$

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Thus, the matrix is:

$AB=\left[\begin{array}{ccc}50&44&-43\\31&16&7\\37&119&-94\end{array}\right]$

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