Can you solve this matrix problem? x+8y=29 2nd equation is 7x+6y=3?

Question

It asks me to find the inverse of matrix A in fraction or integer (not decimal) form. I cannot figure out how to type the matrix into the calculator and find inverse?? Anyone know the answer??

Answer 1

Given A=



|a b|

|c d|



The inverse is computed as



(1 / ad-cd) times the original matirx switched to



|d -b|

|-c a|



So here we have



-1/50 times



|6 -8|

|-7 1|



Which equals the inverse matrix of:



|-6/50 8/50|

|7/50 -1/50|



or reduced to



|-3/25 4/25|

|7/50 -1/50|



By the way, if you have a graphing calculator you should have a key that looks something like



x^-1 (that should be x with -1 as the exponent)



This is the inverse key.



So you enter the matirx into the matrix portion of your calculator, then give it a name like A or B or whatever.



Then to see the inverse you simply hit this inverse key, followed by the matrix name of A or B, etc., and it will give you the inverted matrix.



If it gives it in decimal form, then just enter the 2nd, Math, Frac function and it will change the decimals to fractions.



Have a good day!

Answer 2

use the row reduction method by appending an identity matrix to the right of the matrix

1 8

7 6

giving

1 8 1 0

7 6 0 1

for the above two rows, subtract 7 times the first from the second giving

1 8 1 0

0 -50 -7 1

now divide the bottom row by -50 giving

1 8 1 0

0 1 7/50 -1/50

now, subtract 8 times the new bottom row from the top row

when you are done with this subtraction (I am too lazy to do it) you will get

1 0 a b

0 1 c d

the matrix

a b

c d

is the inverse of the original matrix

Answer 3

x+8y=29 --(1)

7x+6y = 3 ---(2)

Multiply (1) by 7 and substract that from (2)

7x + 56 y - 7x - 6y = 203 - 3

50 y = 200

y = 200/50=4

by substituting this value of y in (1) or (2) you will get x.

x = -3