Back to Multiply matrices and vectors — Problem 2 · Task Set 26

Exercises: Multiply Matrices and Vectors

Work through each section in order. Show your work where indicated.

Grade 9·20 problems·~30 min·Common Core Math - HS Number and Quantity·standard·hsn-vm-c-11

Work through problems with immediate feedback

Recall / Warm-Up

To find the first entry of $A\mathbf{v}$ where $A = \begin{bmatrix}a&b\\c&d\end{bmatrix}$ and $\mathbf{v} = \begin{bmatrix}v_1\\v_2\end{bmatrix}$ , which computation is correct?

$a \cdot v_1$ only (just the top-left entry of $A$ times the top entry of $\mathbf{v}$ )

$a \cdot v_1 + b \cdot v_2$ (row 1 of $A$ dotted with $\mathbf{v}$ )

$c \cdot v_1 + d \cdot v_2$ (row 2 of $A$ dotted with $\mathbf{v}$ )

$a \cdot v_1 \cdot b \cdot v_2$ (product of all relevant entries)