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