Find matrix B, if matrix A=[1/1 5/2], matrix C=[2/1]and AB=3C

 

Asked by shajuamal115 | 25th Oct, 2020, 11:52: AM

Expert Answer:

To find matrix B where A and C are given such that AB = 3C
straight A equals open square brackets table row 1 5 row 1 2 end table close square brackets space space and space straight C equals open square brackets table row 2 row 1 end table close square brackets
straight A to the power of negative 1 end exponent equals open square brackets table row 1 5 row 1 2 end table close square brackets to the power of negative 1 end exponent equals open square brackets table row 2 cell negative 5 end cell row cell negative 1 end cell 1 end table close square brackets
AB equals 3 straight C
Therefore comma space straight B space is space matrix space of space order space 2 cross times 1
Let space straight B equals open square brackets table row straight x row straight y end table close square brackets
rightwards double arrow open square brackets table row 1 5 row 1 2 end table close square brackets space open square brackets table row straight x row straight y end table close square brackets equals 3 open square brackets table row 2 row 1 end table close square brackets equals open square brackets table row 6 row 3 end table close square brackets
rightwards double arrow open square brackets table row cell straight x plus 5 straight y end cell row cell straight x plus 2 straight y end cell end table close square brackets equals open square brackets table row 6 row 3 end table close square brackets
rightwards double arrow straight x plus 5 straight y equals 6 space... space left parenthesis straight i right parenthesis space space and space straight x plus 2 straight y equals 3 space... space left parenthesis ii right parenthesis
rightwards double arrow straight y equals 1 space and space straight x equals 1
Hence comma space straight B equals open square brackets table row 1 row 1 end table close square brackets

Answered by Renu Varma | 26th Oct, 2020, 10:43: AM