In obtaining the solution of the system of equations x+y+z=7, x+2y+3z=16 and x+3y+4z=22 by Cramer's rule, the value of y is obtained by dividing D by D_2, where D=\begin{vmatrix}1&1&1\\ 1&2&3\\ 1&3&4\end{vmatrix}. What is the value of the determinant D_2?

Explanation

In Cramer's rule, D_2 corresponds to the determinant formed by replacing the second column (the y-coefficients) with the constant terms. Thus, D_2 = \begin{vmatrix}1&7&1\\ 1&16&3\\ 1&22&4\end{vmatrix}. Expanding along the first row: 1(64 - 66) - 7(4 - 3) + 1(22 - 16) = -2 - 7(1) + 6 = -3.

Related questions on Matrices & Determinants

• Consider the determinant \Delta=\begin{vmatrix}a_{11}&a_{12}&a_{13}\\ a_{21}&a_{22}&a_{23}\\ a_{31}&a_{32}&a_{33}\end{vmatrix} If $a_{13...
• If A=\begin{pmatrix}1&0&0\\ 0&\cos~\theta&\sin~\theta\\ 0&\sin~\theta&-\cos\theta\end{pmatrix}, then which of the following are correct?...
• If X is a matrix of order 3\times3, Y is a matrix of order 2\times3 and Z is a matrix of order 3\times2, then which of the follo...
• What is the value of a_{11}C_{11}+a_{12}C_{12}+a_{13}C_{13}?
• What is the value of a_{21}C_{11}+a_{22}C_{12}+a_{23}C_{13}?