Calculate the following matrix vector product

(1234)(2−1)=(ab)\begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix} \begin{pmatrix} 2 \ -1 \end{pmatrix}=\begin{pmatrix} a \ b \end{pmatrix}, where

a=[Fill in the blank],
and b=[Fill in the blank],

Question

Calculate the following matrix vector product

(1234)(2−1)=(ab)\begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix} \begin{pmatrix} 2  \ -1 \end{pmatrix}=\begin{pmatrix} a \ b \end{pmatrix}, where

a=[Fill in the blank],
 and b=[Fill in the blank],

BlackTom AI · Accepted Answer

We start by identifying the matrix and the vector to multiply: the matrix is [[1, 2], [3, 4]] and the vector is [2, -1].

Next, perform the matrix-vector multiplication step by step. Multiply the first row of the matrix by the vector to obtain the first component a:
- a = 1*2 + 2*(-1) = 2 + (-2) = 0.

Then multiply the second row of the matrix by the vector to obtain the second component b:
- b = 3*2 + 4*(-1) = 6 + (-4) = 2.

Thus, the resulting vector is [a, b] = [0, 2].

If you are filling in the blanks, a should be 0 and b should be 2.

To check, you can re-verify the multiplication: the product of the matrix with the vector yields (0, 2) as computed above.

Note: Each entry of the result comes from the dot product of a matrix row with the given vector, which is the standard procedure for matrix-vector multiplication.

MAT223H1S Winter 2025 Reading Quiz 2

Calculate the following matrix vector product (1234)(2−1)=(ab)\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \begin{pmatrix} 2 \\ -1 \end{pmatrix}=\begin{pmatrix} a \\ b \end{pmatrix}, where a=[Fill in the blank], and b=[Fill in the blank],

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