The system of equations 2x + 6y = -11,6x + 20 | vedclass

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Question

(A) Given equations are:$2x + 6y + 0z = -11$$6x + 20y - 6z = -3$$0x + 6y - 18z = -1$We calculate the determinant $D$ of the coefficient matrix:$D = \b

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inconsistent

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(A) Given equations are:$2x + 6y + 0z = -11$$6x + 20y - 6z = -3$$0x + 6y - 18z = -1$We calculate the determinant $D$ of the coefficient matrix:$D = \begin{vmatrix} 2 & 6 & 0 \ 6 & 20 & -6 \ 0 & 6 & -18 \end{vmatrix}$$D = 2(20 	imes (-18) - (-6) 	imes 6) - 6(6 	imes (-18) - 0) + 0$$D = 2(-360 + 36) - 6(-108)$$D = 2(-324) + 648 = -648 + 648 = 0$Since $D = 0$,the system is either inconsistent or has infinitely many solutions. We check $D_1$:$D_1 = \begin{vmatrix} -11 & 6 & 0 \ -3 & 20 & -6 \ -1 & 6 & -18 \end{vmatrix}$$D_1 = -11(20 	imes (-18) - (-6) 	imes 6) - 6((-3) 	imes (-18) - (-1) 	imes (-6))$$D_1 = -11(-360 + 36) - 6(54 - 6)$$D_1 = -11(-324) - 6(48) = 3564 - 288 = 3276 
eq 0$Since $D = 0$ and $D_1 
eq 0$,the system of equations is inconsistent.

The system of equations $2x + 6y = -11$,$6x + 20y - 6z = -3$ and $6y - 18z = -1$ are

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