Find the matrix A, which satisfy the matrix equation,

Asked by Topperlearning User | 2nd May, 2016, 11:08: AM

Expert Answer:

The matrix equation is given by

Inverse of B:
Inverse of C:
C equals open square brackets table row cell negative 4 end cell 3 row 5 cell negative 4 end cell end table close square brackets comma space open vertical bar C close vertical bar equals 16 minus 15 equals 1
C to the power of negative 1 end exponent equals fraction numerator 1 over denominator open vertical bar C close vertical bar end fraction a d j space C
rightwards double arrow C to the power of negative 1 end exponent equals 1 over 1 open square brackets table row cell negative 4 end cell cell negative 3 end cell row cell negative 5 end cell cell negative 4 end cell end table close square brackets equals open square brackets table row cell negative 4 end cell cell negative 3 end cell row cell negative 5 end cell cell negative 4 end cell end table close square brackets
N o w space A equals B to the power of negative 1 end exponent C to the power of negative 1 end exponent equals 1 over 9 open square brackets table row 4 cell negative 1 end cell row cell negative 3 end cell 3 end table close square brackets open square brackets table row cell negative 4 end cell cell negative 3 end cell row cell negative 5 end cell cell negative 4 end cell end table close square brackets
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 over 9 open square brackets table row cell negative 16 plus 5 end cell cell negative 12 plus 4 end cell row cell 12 minus 15 end cell cell 9 minus 12 end cell end table close square brackets
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 over 9 open square brackets table row cell negative 11 end cell cell negative 8 end cell row cell negative 3 end cell cell negative 3 end cell end table close square brackets

 

Answered by  | 2nd May, 2016, 01:08: PM