Questions: × 1 / 6 Unit Exam-Matrices Find the product. [6 0 4 -3 -3 -2] [3 -5]

Transcript text: ■ $\times$ $1 / 6$ Unit Exam-Matrices Find the product. \[ \left[\begin{array}{rr} 6 & 0 \\ 4 & -3 \\ -3 & -2 \end{array}\right]\left[\begin{array}{r} 3 \\ -5 \end{array}\right] \]

Solution

Solution Steps

Step 1: Matrix Multiplication

Multiply the first row of the first matrix by the column of the second matrix:

[6 * 3 + 0 * -5] = [18]

Step 2: Matrix Multiplication

Multiply the second row of the first matrix by the column of the second matrix:

[4 * 3 + (-3) * (-5)] = [12 + 15] = [27]

Step 3: Matrix Multiplication

Multiply the third row of the first matrix by the column of the second matrix:

[(-3) * 3 + (-2) * (-5)] = [-9 + 10] = [1]

Final Answer

\begin{bmatrix} 18 \\ 27 \\ 1 \end{bmatrix}

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