Compute the product. begin{bmatrix}0 & -4 & 5 end{bmatrix}begin{bmatrix}x y z end{bmatrix}

Question
Matrices
asked 2021-03-01
Compute the product.
\(\begin{bmatrix}0 & -4 & 5 \end{bmatrix}\begin{bmatrix}x \\ y \\ z \end{bmatrix}\)

Answers (1)

2021-03-02
Step 1
Matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix.
In order to multiply two matrices, we need to do dot product of rows to column.
Step 2
We have the matrices as
\(\begin{bmatrix}0 & -4 & 5 \end{bmatrix}\begin{bmatrix}x \\ y \\ z \end{bmatrix}\)
Here number of column for first matrix is same as number of rows of second matrix. Therefore multiplication of these two matrices took place as
\(\begin{bmatrix}0 & -4 & 5 \end{bmatrix}\begin{bmatrix}x \\ y \\ z \end{bmatrix} =\begin{bmatrix}(0)(x)+(-4)(y)+(5)(z) \end{bmatrix}\)
\(\begin{bmatrix} 0-4y+5z \end{bmatrix}\)
\(\begin{bmatrix} -4y+5z \end{bmatrix}\)
Hence, matrix after multiplication of matrices \(\begin{bmatrix}0 & -4 & 5 \end{bmatrix}\begin{bmatrix}x \\ y \\ z \end{bmatrix} \text{ is } \begin{bmatrix} -4y+5z \end{bmatrix}\)
0

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