If the set of equations x+2y+3z=6,x+3y+5z=9,a | vedclass

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(B) For a system of linear equations to have a unique solution,the determinant of the coefficient matrix must be non-zero. The coefficient matrix is $

Vedclass · Accepted Answer

$a 
eq 8, b \in R$

Vedclass · Answer

(B) For a system of linear equations to have a unique solution,the determinant of the coefficient matrix must be non-zero. The coefficient matrix is $A = \begin{bmatrix} 1 & 2 & 3 \ 1 & 3 & 5 \ 2 & 5 & a \end{bmatrix}$. The condition for a unique solution is $|A| 
eq 0$. $|A| = 1(3a - 25) - 2(a - 10) + 3(5 - 6) 
eq 0$. $|A| = 3a - 25 - 2a + 20 - 3 
eq 0$. $|A| = a - 8 
eq 0$. Therefore,$a 
eq 8$. Since the value of $b$ does not affect the determinant of the coefficient matrix,$b$ can be any real number $(b \in R)$. Thus,the condition is $a 
eq 8$ and $b \in R$.

If the set of equations $x+2y+3z=6$,$x+3y+5z=9$,and $2x+5y+az=b$ has a unique solution,then:

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