find inverse of matrx using elementary row operation

(i)   1     2

       2    -1

ii )    2      5

       -3      1

ignore ithe absence of braclet and consider it in square bracket

also sate the key method to find matrix

Asked by haroonrashidgkp | 26th Mar, 2018, 09:11: PM

Expert Answer:

begin mathsize 16px style straight A equals open square brackets table row 1 2 row 2 cell negative 1 end cell end table close square brackets
open vertical bar straight A close vertical bar equals negative 1 minus 4 equals negative 5 not equal to 0
straight A to the power of negative 1 end exponent space exist.
rightwards double arrow straight A straight A to the power of negative 1 end exponent equals straight I
rightwards double arrow open square brackets table row 1 2 row 2 cell negative 1 end cell end table close square brackets straight A to the power of negative 1 end exponent equals open square brackets table row 1 0 row 0 1 end table close square brackets
straight R subscript 2 minus 2 straight R subscript 1
rightwards double arrow open square brackets table row 1 2 row 0 cell negative 5 end cell end table close square brackets straight A to the power of negative 1 end exponent equals open square brackets table row 1 0 row cell negative 2 end cell 1 end table close square brackets
fraction numerator straight R subscript 2 over denominator negative 5 end fraction
rightwards double arrow open square brackets table row 1 2 row 0 1 end table close square brackets straight A to the power of negative 1 end exponent equals open square brackets table row 1 0 row cell 2 over 5 end cell cell fraction numerator negative 1 over denominator 5 end fraction end cell end table close square brackets
straight R subscript 1 minus 2 straight R subscript 2
rightwards double arrow open square brackets table row 1 0 row 0 1 end table close square brackets straight A to the power of negative 1 end exponent equals open square brackets table row cell 1 fifth end cell cell 2 over 5 end cell row cell 2 over 5 end cell cell fraction numerator negative 1 over denominator 5 end fraction end cell end table close square brackets
rightwards double arrow straight A to the power of negative 1 end exponent equals 1 fifth open square brackets table row 1 2 row 2 cell negative 1 end cell end table close square brackets
Similarly space you space can space find space inverse space of space second space matrix. end style

Answered by Sneha shidid | 27th Mar, 2018, 09:05: AM