The following system of equations 3x - 7y + 5 | vedclass

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(B) To determine the nature of the system,we write it in the matrix form $AX = B$,where $A = \begin{bmatrix} 3 & -7 & 5 \ 3 & 1 & 5 \ 2 & 3 & 5 \end

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consistent with a unique non-trivial solution

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(B) To determine the nature of the system,we write it in the matrix form $AX = B$,where $A = \begin{bmatrix} 3 & -7 & 5 \ 3 & 1 & 5 \ 2 & 3 & 5 \end{bmatrix}$.We calculate the determinant $|A|$:$|A| = 3(1 	imes 5 - 5 	imes 3) - (-7)(3 	imes 5 - 5 	imes 2) + 5(3 	imes 3 - 1 	imes 2)$$|A| = 3(5 - 15) + 7(15 - 10) + 5(9 - 2)$$|A| = 3(-10) + 7(5) + 5(7)$$|A| = -30 + 35 + 35 = 40$.Since $|A| 
eq 0$,the system has a unique solution.By Cramer's rule or matrix inversion,we can find the values of $x, y, z$. Since the constants on the right side are non-zero,the solution is non-trivial.Thus,the system is consistent with a unique non-trivial solution.

The following system of equations $3x - 7y + 5z = 3$,$3x + y + 5z = 7$,and $2x + 3y + 5z = 5$ is:

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