Class 12 Maths Matrices Multiplication of Matrices by scalar

Multiplication of Matrices by scalar

If it is told that the apple & Orange that Tina, Abdul & Minu has is doubled, then we have to multiply each of these matrices elements by 2. Here 2 is a scalar quantity.

 

If A = [aij] m × n is a matrix and k is a scalar, then kA is another matrix which is obtained by multiplying each element of A by the scalar k.

 

The negative of a matrix is denoted by –A. We define –A = (– 1) A.

 

Numerical:

 

Solution: Solving we get

X=3, y=6, z=9 & t=6

 

Properties of scalar multiplication of a matrix

If A = [aij] & B = [bij] be two matrices of same order, say m × n, and k and l are scalars, then

  • k(A +B) = kA + kB,
  • (k + l)A = k A + l A

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