solve the matrix equation open square brackets table row 10 8 row 2 8 end table close square bracketsX=open square brackets table row 1 cell negative 2 end cell row 1 3 end table close square brackets,where X is a 2x2 matrix.

Asked by savi1405 | 28th Apr, 2016, 05:11: PM

Expert Answer:

open square brackets table row 10 8 row 2 8 end table close square brackets straight X equals open square brackets table row 1 cell negative 2 end cell row 1 3 end table close square brackets

Let space space straight A equals open square brackets table row 10 8 row 2 8 end table close square brackets comma space straight B equals open square brackets table row 1 cell negative 2 end cell row 1 3 end table close square brackets
open square brackets table row 10 8 row 2 8 end table close square brackets straight X equals open square brackets table row 1 cell negative 2 end cell row 1 3 end table close square brackets
rightwards double arrow AX equals straight B
open vertical bar straight A close vertical bar equals open vertical bar table row 10 8 row 2 8 end table close vertical bar equals 80 minus 16 equals 64 not equal to 0
So comma space the space solution space of space will space be space unique space and space is space given space by space straight X equals straight A to the power of negative 1 end exponent straight B
Let space straight C subscript ij space be space the space co minus factors space of space elements space straight a subscript ij space in space straight A equals open square brackets space straight a subscript ij close square brackets.
Then comma space space space straight C subscript 11 equals left parenthesis negative 1 right parenthesis to the power of 1 plus 1 end exponent left parenthesis 8 right parenthesis equals 8
space straight C subscript 12 equals left parenthesis negative 1 right parenthesis to the power of 1 plus 2 end exponent left parenthesis 2 right parenthesis equals negative 2 comma space space space space space straight C subscript 22 equals left parenthesis negative 1 right parenthesis to the power of 2 plus 2 end exponent left parenthesis 10 right parenthesis equals 10
straight C subscript 21 equals left parenthesis negative 1 right parenthesis to the power of 2 plus 1 end exponent left parenthesis 8 right parenthesis equals negative 8
rightwards double arrow adjA equals open square brackets table row 8 cell negative 2 end cell row cell negative 8 end cell 10 end table close square brackets to the power of straight T equals open square brackets table row 8 cell negative 8 end cell row cell negative 2 end cell 10 end table close square brackets
So comma space straight A to the power of negative 1 end exponent equals fraction numerator 1 over denominator open vertical bar straight A close vertical bar end fraction adjA equals 1 over 64 open square brackets table row 8 cell negative 8 end cell row cell negative 2 end cell 10 end table close square brackets equals open square brackets table row cell 1 over 8 end cell cell space space space minus 1 over 8 end cell row cell negative 1 over 32 end cell cell space space space space space space 5 over 32 end cell end table close square brackets
rightwards double arrow straight X equals space straight A to the power of negative 1 end exponent straight B equals open square brackets table row cell 1 over 8 end cell cell space space space minus 1 over 8 end cell row cell negative 1 over 32 end cell cell space space space space space space 5 over 32 end cell end table close square brackets open square brackets table row 1 cell negative 2 end cell row 1 3 end table close square brackets equals open square brackets table row 0 cell space fraction numerator negative 5 over denominator 8 end fraction end cell row cell 1 over 8 end cell cell space space space 17 over 32 end cell end table close square brackets

Answered by Rebecca Fernandes | 29th Apr, 2016, 10:13: AM