How to Inverse this 3x3 matrix Using Gauss-Jordan

Question

⌈10  20  30⌉

|20  40  50|

⌊30  50  60⌋

Answer 1

Hard to type matrix here but anyway. First the idea: You have matrix A. Now you write this way A|I, I -unit matrix.

Apply row operations to this matrix until the left side is reduced to I.

 

[10 20 30]|[1 0 0]

[20 40 50]|[0 1 0]

[30 50 60]|]0 0 1]

 

Next step, apply row operations to the left side. Lets for now, multiply the  first row by -2 and and add to the second and then multiply the it by -3 and add to the third row, etc...

 

At the end you have go get unit matrix in the left and 

[1/10  -3/10,   1/5]

[-3/10  3/10, -1/10]

[1/5    -1/10    0]

 

This is the inverse of your matrix.

 

 

 

 

 

 

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