ICSE Class 10 Answered

If A= $begin mathsize 12px style open square brackets table row 2 cell negative 1 end cell row cell negative 6 end cell 5 end table close square brackets end style$ and B is a null matrix, find the value of A + 2B + IA.

Asked by Topperlearning User | 21 Sep, 2017, 01:11: PM

Expert Answer

Given A = _{$begin mathsize 12px style open square brackets table row 2 cell negative 1 end cell row cell negative 6 end cell 5 end table close square brackets end style$}and B = $begin mathsize 12px style open square brackets table row 0 0 row 0 0 end table close square brackets end style$

We know that on multiplying any constant with the null matrix,

the resultant matrix is a null matrix.

2B = 0

Also, the product of any matrix with the Identity matrix is the matrix itself.

Hence IA = A.

A + 2B + IA = A + 0 +A = 2A = 2 $open square brackets table row size 12px 2 cell size 12px minus size 12px 1 end cell row cell size 12px minus size 12px 6 end cell size 12px 5 end table close square brackets$ = _{$open square brackets table row size 12px 4 cell size 12px minus size 12px 2 end cell row cell size 12px minus size 12px 12 end cell size 12px 10 end table close square brackets$}