How Do You Multiply a Matrix by a Scalar?

-3 is a scalar
A scalar doesn't have dimensions, so we can multiply a scalar by a matrix with any dimensions
Multiply each element of the matrix by the scalar -3
-3•5 = -15
-3•(-5) = 15
-3•0 = 0
-3•12 = -36
Notice that the answer matrix has the same dimensions as the matrix we started with, 2x2

1. Scalars don't have dimensions, so we can multiply a scalar by a matrix with any dimensions
1. The matrix has four elements: 5, -5, 0, and 12
2. So we need to multiply -3•5, -3•(-5), -3•0, and -3•12
3. Each product goes in the same place in the new matrix as it did in the original one
1. Now we can just perform all that multiplication to simplify
1. -3•5 = -15
2. -3•(-5) = 15
3. -3•0 = 0
4. -3•12 = -36
1. In scalar multiplication, the dimensions of the new matrix will always be the same as the original

Multiply the scalar, -3, by the matrix in the diagram.