Matrix scalar multiplication
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Definition.
The product of the matrix A to number k is a matrix B = k · A of the same size derived from matrix A by multiplying every entry of A by k:bi,j = k · ai,j
Properties of matrix scalar multiplication
- 1 · A = A
- 0 · A = Θ, where Θ - zero matrix
- k · (A + B) = k · A + k · B
- (k + n) · A = k · A + n · A
- (k · n) · A = k · (n · A)
Examples of matrix scalar multiplication
Example 1.
| Find the product of matrix A = |  |
4 | 2 |  |
and the number 5. |
| 9 | 0 |
Solution:
| 5·A= | 5· | |
4 | 2 | |
= | |
5·4 | 5·2 | |
= | |
20 | 10 | |
| 9 | 0 | 5·9 | 5·0 | 45 | 0 |
Example 2
| Find the product of matrix A = | |
2 | -2 | |
and the number (-2). |
| -1 | 0 | ||||
| 5 | -1 |
Solution:
| (-2)·A = (-2)· | |
2 | -2 | |
= | |
(-2)·2 | (-2)·(-2) | |
= | |
-4 | 4 | |
| -1 | 0 | (-2)·(-1) | (-2)·0 | 2 | 0 | |||||||||
| 5 | -1 | (-2)·5 | (-2)·(-1) | -10 | 2 |
MatrixMatrix Definition. Main informationSystem of linear equations - matrix formTypes of matricesMatrix scalar multiplicationAddition and subtraction of matricesMatrix multiplicationTranspose matrixElementary matrix operationsDeterminant of a matrixMinors and cofactors of a matrixInverse matrixLinearly dependent and independent rowsRank of a matrix
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