Question

Solve the following: 1. If [ 3 4 1 ] + [ 2 1 −2 ] − [ 1 1 −2 ] = [ 5 0 7 3 ], find the values of , and . 2. Find the value of , given that 2 = , = [ 2 12 0 1 ] and = [ 4 0 1 ] 3. Given A = [ 2 −6 2 0 ], B = [ −3 2 4 0 ] and C = [ 4 0 0 2 ]. Find the matrix X such that A + 2X = 2B + C. 4. Given A = [ 3 −2 −1 4 ] , B = [ 6 1 ] , C = [ −4 5 ] and D = [ 2 2 ]. Find : AB + 2C – 4D 5. If A = [ 3 1 4 0 ] , B = [ 1 −2 2 3 ] and 3A – 5B + 2X = [ 4 3 0 1 ] ; find the matrix X . 6. If P = [ 6 −2 4 −6 ] and Q = [ 5 3 2 0 ] , find the matrix M such that 2Q – 3P – 3M = 0. 7. Find and , if : [ 3 −2 −1 4 ][ 2 1 ] + 2 [ −4 5 ] = 4 [ 2 ] 8. Find and , if : [ 3 4 ][ 2 1 ] = [ 5 12]​

Answer 1

Answer:

Given, [1 x 1]1×3 ⎣⎢⎢⎡1215353212⎦⎥⎥⎤3×3 ⎣⎢⎢⎡12x⎦⎥⎥⎤3×1=O 

⇒ [1+2x+153+5x+32+x+2]⎣⎢⎢⎡12x⎦⎥⎥⎤=O 

⇒ [16+2x+153+5x+32+x+2] ⎣⎢⎢⎡12x⎦⎥⎥⎤=O