Examine the consistency of the system of equa | vedclass

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(A) The given system of equations is:$5x - y + 4z = 5$$2x + 3y + 5z = 2$$5x - 2y + 6z = -1$The system can be written as $AX = B$,where:$A = \begin{bma

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Consistent

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(A) The given system of equations is:$5x - y + 4z = 5$$2x + 3y + 5z = 2$$5x - 2y + 6z = -1$The system can be written as $AX = B$,where:$A = \begin{bmatrix} 5 & -1 & 4 \ 2 & 3 & 5 \ 5 & -2 & 6 \end{bmatrix}$,$X = \begin{bmatrix} x \ y \ z \end{bmatrix}$,$B = \begin{bmatrix} 5 \ 2 \ -1 \end{bmatrix}$Now,calculate the determinant $|A|$:$|A| = 5(3 	imes 6 - (-2) 	imes 5) - (-1)(2 	imes 6 - 5 	imes 5) + 4(2 	imes (-2) - 5 	imes 3)$$|A| = 5(18 + 10) + 1(12 - 25) + 4(-4 - 15)$$|A| = 5(28) + 1(-13) + 4(-19)$$|A| = 140 - 13 - 76 = 51$Since $|A| = 51 
eq 0$,the matrix $A$ is non-singular and invertible.Therefore,the system of equations has a unique solution and is consistent.

Examine the consistency of the system of equations: $5x - y + 4z = 5$,$2x + 3y + 5z = 2$,and $5x - 2y + 6z = -1$.

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