JEE Main & Advanced Mathematics Determinants & Matrices Scalar Multiplication of Matrices

Scalar Multiplication of Matrices

Category : JEE Main & Advanced

 Let \[A={{[{{a}_{ij}}]}_{m\times n}}\]be a matrix and k be a number, then the matrix which is obtained by multiplying every element of A by k is called scalar multiplication of A by k and it is denoted by kA.


Thus, if \[A={{[{{a}_{ij}}]}_{m\times n}}\], then \[kA=Ak={{[k{{a}_{ij}}]}_{m\times n}}\].


Properties of scalar multiplication


If A, B are matrices of the same order and \[\lambda ,\,\mu \] are any two scalars then


(i) \[\lambda (A+B)=\lambda A+\lambda B\]                     


(ii) \[(\lambda +\mu )A=\lambda A+\mu A\]


(iii) \[\lambda (\mu A)=(\lambda \mu A)=\mu (\lambda A)\]


(iv) \[(-\lambda A)=-(\lambda A)=\lambda \,(-A)\]


  • All the laws of ordinary algebra hold for the addition or subtraction of matrices and their multiplication by scalars.

You need to login to perform this action.
You will be redirected in 3 sec spinner