Final answer:
The product of -4x and the matrix [8 -1 -5 g] is calculated by multiplying each matrix element by -4x, resulting in the matrix [-32x, 4x, 20x, -4xg].
Step-by-step explanation:
The student's question involves finding the product of a number and a matrix. To calculate the product when multiplying a scalar (a single number) by a matrix, you multiply each entry of the matrix by the scalar. In this case, the scalar is -4x and the matrix is [8 -1 -5 g], so the resulting product will be a matrix where each of these four values has been multiplied by -4x:
- (-4x) × 8 = -32x
- (-4x) × (-1) = 4x
- (-4x) × (-5) = 20x
- (-4x) × g = -4xg
Therefore, the product is the matrix [-32x, 4x, 20x, -4xg].