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Question

Solve the following system of linear equations using matrix method: 3x+y+z=1,2x+2z=0,5x+5y+2z=2.

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Solution

The system of linear equations are
3x+y+z=1
2x+2z=0
5x+5y+2x=2
This corresponds to 311202552xyz=102
The augmented matrix is 311120205522
Applying elementary row operations,
311120205522R1R1R2111120205522
R2R22R1
R3R35R1
111101210073R2R22111102420073
R1R1R2
101001210073R3R37⎢ ⎢ ⎢1010012100137⎥ ⎥ ⎥
R2R2+2R3
R1R1R3
⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢100370101700137⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
So, x=37,y=17,z=37

1155204_1110883_ans_c469474995b54c8aa4682ae3f4dc60b1.jpg

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