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# How to solve this matrix by hand?

I don't want you to solve this problem step by step just show me the way how it's solved "the idea"

Thanks!

### 3 Answers

- cryptogramcornerLv 61 month ago
Convert the matrix into upper triangular form and then do back substitution. The first step would be to get rid of the 2 at the beginning of the 2nd row. You can do this by multiplying the first row by 2 and adding it to the 2nd. You end up with a 2nd row that is something like [0 1 2 0 0] with a right hand side of -15. You then want to get rid of the 2 in the 3rd row, which you can do by multiplying your new row 2 by -2 and adding it to the 3rd row. Continue in this fashion until the last row start with 4 zeroes. The number in the 5th column can then be divided into the right hand side to get x5. Once you know x5 you can use it in row 4, and solve for x4, and continue working your way back up to get x3, x2, and finally x1.

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- stanschimLv 71 month ago
One way is to carry out matrix multiplication on the left side. Setting each of the 5 results equal to the value on the right side. You will have 5 equations in 5 unknowns and be able to solve for the unknowns.

Another way is to find the inverse matrix for the 5 by 5 matrix on the left side. If you multiply this inverse matrix by the column on the right side, you will also obtain the unknowns.

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