Q-15

Asked by majethiyarishat9566.12sdatl | 4th May, 2020, 05:34: PM

Expert Answer:

Question: Given A = [1,-1,0,2,3,4,0,1,2] and B = [2,2,-4,-4,2,-4,2,-1,5]. Verify that BA = 9I. Using this result solve the set of linear equations
Solution: 
 B A equals open square brackets table row 2 2 cell negative 4 end cell row cell negative 4 end cell 2 cell negative 4 end cell row 2 cell negative 1 end cell 5 end table close square brackets open square brackets table row 1 cell negative 1 end cell 0 row 2 3 4 row 0 1 2 end table close square brackets equals open square brackets table row cell 2 plus 4 end cell cell negative 2 plus 6 minus 4 end cell cell 8 minus 8 end cell row cell negative 4 plus 4 end cell cell 4 plus 6 minus 4 end cell cell 8 minus 8 end cell row cell 2 minus 2 end cell cell negative 2 minus 3 plus 5 end cell cell negative 4 plus 10 end cell end table close square brackets equals open square brackets table row 6 0 0 row 0 6 0 row 0 0 6 end table close square brackets equals 6 open square brackets table row 1 0 0 row 0 1 0 row 0 0 1 end table close square brackets equals 6 I
rightwards double arrow A to the power of negative 1 end exponent equals 1 over 6 B
G i v e n space e q u a t i o n s space a r e space x minus y equals 3 comma space 2 x plus 3 y plus 4 z equals 17 comma space y plus 2 z equals 7
rightwards double arrow open square brackets table row 1 cell negative 1 end cell 0 row 2 3 4 row 0 1 2 end table close square brackets open square brackets table row x row y row z end table close square brackets equals open square brackets table row 3 row 17 row 7 end table close square brackets
rightwards double arrow open square brackets table row x row y row z end table close square brackets equals open square brackets table row 1 cell negative 1 end cell 0 row 2 3 4 row 0 1 2 end table close square brackets to the power of negative 1 end exponent open square brackets table row 3 row 17 row 7 end table close square brackets
rightwards double arrow open square brackets table row x row y row z end table close square brackets equals 1 over 6 open square brackets table row 2 2 cell negative 4 end cell row cell negative 4 end cell 2 cell negative 4 end cell row 2 cell negative 1 end cell 5 end table close square brackets open square brackets table row 3 row 17 row 7 end table close square brackets equals 1 over 6 open square brackets table row cell 6 plus 34 minus 28 end cell row cell negative 12 plus 34 minus 28 end cell row cell 6 minus 17 plus 35 end cell end table close square brackets equals 1 over 6 open square brackets table row 12 row cell negative 6 end cell row 24 end table close square brackets equals open square brackets table row 2 row cell negative 1 end cell row 4 end table close square brackets
therefore space x equals 2 comma space y equals negative 1 comma space z equals 4

Answered by Renu Varma | 9th May, 2020, 01:34: PM