Multiplying a Matrix by a Number

rows

1

2

3

4

5

columns

1

2

3

4

5

new number, matrix

k = -2,

A =

2	2	-4
2	0	-4
-2	1	-3
5	1	2

k × A =

-2 × (2)	-2 × (2)	-2 × (-4)
-2 × (2)	-2 × (0)	-2 × (-4)
-2 × (-2)	-2 × (1)	-2 × (-3)
-2 × (5)	-2 × (1)	-2 × (2)

=

-4	-4	8
-4	0	8
4	-2	6
-10	-2	-4

To multiply a matrix by a number, multiply each entry by the number.

If there is only one column or only one row, the matrix is a column or a row vector.

External Links

Vector Addition (Wolfram MathWorld)

Matrix Addition (Wolfram MathWorld)

Matrix Multiplication (Wolfram MathWorld)

Matrix Multiplication

Permanent Citation

George Beck

"Multiplying a Matrix by a Number"
http://demonstrations.wolfram.com/MultiplyingAMatrixByANumber/
Wolfram Demonstrations Project
Published: June 11, 2018