Solve system of linear equations, using matrix method, in Exercises 7 to 14.
$$
\begin{array}{l}
x-y+2 z=7 \\
3 x+4 y-5 z=-5 \\
2 x-y+3 z=12
\end{array}
$$

Answer

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Algebra

NCERT Class 12 Part 1 - Math

Chapter 4

Determinants

Section 6

Adjoint and Inverse of a Matrix

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Video Transcript

in the question, we have to solve the human system of linear equations using the metrics method. Where the questions are x minus five plus said is equals to four two X plus y minus three, said as opposed to zero, X plus Y. Plus that is a two. Now moving towards the solution, the given system of equations can be represented as a X. Supposed to be where they will be the metrics with the element 1 -1, 1, 2, -3, 1, 1, 1, and X is the microbes with the element X. Why is that? and paste the metrics with element for 0 to and no. First we will be finding the determinant for the metrics there, which will be calculated as four plus five plus one, which is equivalent to 10. Now, as the determinant of my tricks, A. S 10 is not equal to zero. So the given system of equations comes out to me consistent and so we can write your ex metrics as a N. Boss into the be my cracks. Now as we know that the N. A inverse is found out by one divided by the determinant of my trixie into the joint of the matrix A. So we will be putting the values here, you will get your X matrix equals to one by 10 and 24 to minus 505 one minus 23 and to the bee matrix, which is 402 So solving this, you will get your answer as X will be to why will be minus one? And that will be one. Thank you.

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