JEE Main & Advanced Mathematics 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.

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