# Chapter 10 - 10.2 - Operations with Matrices - 10.2 Exercises - Page 725: 50

Part A: $\begin{bmatrix} 6\\ 18\\ \end{bmatrix}$ Part B: Not possible. Part C: Not possible.

#### Work Step by Step

A has 2 rows and 3 columns (2 x 3). B has 3 rows and 1 column (3 x 1). Part A: $\begin{bmatrix} 1(3) + 3(3) + (-2)(3)\\ (-5)(3) + 10(3) + 1(3)\\ \end{bmatrix}$ = $\begin{bmatrix} 3 + 9 - 6\\ -15 + 30 + 3\\ \end{bmatrix}$ = $\begin{bmatrix} 6\\ 18\\ \end{bmatrix}$ Part B: Since the number of columns in B does not equal the number of rows in A, BA is not possible. Part C: Since the number of columns in A does not equal the number of rows in A, AA is not possible.

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