We can multiply the elements of the given matrix A by a non-zero number k to obtain a new matrix kA whose elements are multiplied by k. The matrix kA is called scalar multiplication of A.

We can multiply the elements of the given matrix *A* by a non-zero number *k* to obtain a new matrix *kA* whose elements are multiplied by *k*. The matrix *kA* is called scalar multiplication of *A*.

Thus if *A* = (*aij* )*m* ×*n* then , *kA* = (*kaij* )*m* ×*n* for all *i* = 1,2,…,*m* and for all *j* = 1,2,…,*n*.

If A = then Find 2A+B.

Since *A* and *B* have same order 3 ×3 , 2*A* + *B* is defined.

Example 3.61

*Solution*

Since *A, B* are of the same order 3 ×3 , subtraction of 4*A* and 3*B* is defined.

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10th Mathematics : UNIT 3 : Algebra : Multiplication of Matrix by a Scalar |

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