79246 If \(A=\left|\begin{array}{lll}x & 1 & 1 \\ 1 & x & 1 \\ 1 & 1 & x\end{array}\right|\) and \(B=\left|\begin{array}{ll}x & 1 \\ 1 & x\end{array}\right|\), then \(\frac{d A}{d x}=\)

79247 The value of ' \(a\) ' for which the system of equations
\(a^{3} x+(a+1)^{3} y+(a+2)^{3} z=0 \\ a x+(a+1) y+(a+2) z=0 \\ x+y+z=0\)
has a non-zero solution is

79248 If \(\left[\begin{array}{lll}1 & 3 & 3 \\ 1 & 4 & 4 \\ 1 & 3 & 4\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}12 \\ 15 \\ 13\end{array}\right]\), then the value of \(x, y\), respectively are

79250 The system of linear equations \(x+y+z=2,2 x\) \(+y-z=3,3 x+2 y+k z=4\) has a unique solution if

79251 The system of equations \(k x+2 y-z=1,(k-1)\) \(y-2 z=2\) and \((k+2) z=3\) have a unique solution if \(k\) equals

79246 If \(A=\left|\begin{array}{lll}x & 1 & 1 \\ 1 & x & 1 \\ 1 & 1 & x\end{array}\right|\) and \(B=\left|\begin{array}{ll}x & 1 \\ 1 & x\end{array}\right|\), then \(\frac{d A}{d x}=\)

79247 The value of ' \(a\) ' for which the system of equations
\(a^{3} x+(a+1)^{3} y+(a+2)^{3} z=0 \\ a x+(a+1) y+(a+2) z=0 \\ x+y+z=0\)
has a non-zero solution is

79248 If \(\left[\begin{array}{lll}1 & 3 & 3 \\ 1 & 4 & 4 \\ 1 & 3 & 4\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}12 \\ 15 \\ 13\end{array}\right]\), then the value of \(x, y\), respectively are

79250 The system of linear equations \(x+y+z=2,2 x\) \(+y-z=3,3 x+2 y+k z=4\) has a unique solution if

79251 The system of equations \(k x+2 y-z=1,(k-1)\) \(y-2 z=2\) and \((k+2) z=3\) have a unique solution if \(k\) equals

79246 If \(A=\left|\begin{array}{lll}x & 1 & 1 \\ 1 & x & 1 \\ 1 & 1 & x\end{array}\right|\) and \(B=\left|\begin{array}{ll}x & 1 \\ 1 & x\end{array}\right|\), then \(\frac{d A}{d x}=\)

79247 The value of ' \(a\) ' for which the system of equations
\(a^{3} x+(a+1)^{3} y+(a+2)^{3} z=0 \\ a x+(a+1) y+(a+2) z=0 \\ x+y+z=0\)
has a non-zero solution is

79248 If \(\left[\begin{array}{lll}1 & 3 & 3 \\ 1 & 4 & 4 \\ 1 & 3 & 4\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}12 \\ 15 \\ 13\end{array}\right]\), then the value of \(x, y\), respectively are

79250 The system of linear equations \(x+y+z=2,2 x\) \(+y-z=3,3 x+2 y+k z=4\) has a unique solution if

79251 The system of equations \(k x+2 y-z=1,(k-1)\) \(y-2 z=2\) and \((k+2) z=3\) have a unique solution if \(k\) equals

79246 If \(A=\left|\begin{array}{lll}x & 1 & 1 \\ 1 & x & 1 \\ 1 & 1 & x\end{array}\right|\) and \(B=\left|\begin{array}{ll}x & 1 \\ 1 & x\end{array}\right|\), then \(\frac{d A}{d x}=\)

79247 The value of ' \(a\) ' for which the system of equations
\(a^{3} x+(a+1)^{3} y+(a+2)^{3} z=0 \\ a x+(a+1) y+(a+2) z=0 \\ x+y+z=0\)
has a non-zero solution is

79248 If \(\left[\begin{array}{lll}1 & 3 & 3 \\ 1 & 4 & 4 \\ 1 & 3 & 4\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}12 \\ 15 \\ 13\end{array}\right]\), then the value of \(x, y\), respectively are

79250 The system of linear equations \(x+y+z=2,2 x\) \(+y-z=3,3 x+2 y+k z=4\) has a unique solution if

79251 The system of equations \(k x+2 y-z=1,(k-1)\) \(y-2 z=2\) and \((k+2) z=3\) have a unique solution if \(k\) equals

79246 If \(A=\left|\begin{array}{lll}x & 1 & 1 \\ 1 & x & 1 \\ 1 & 1 & x\end{array}\right|\) and \(B=\left|\begin{array}{ll}x & 1 \\ 1 & x\end{array}\right|\), then \(\frac{d A}{d x}=\)

79247 The value of ' \(a\) ' for which the system of equations
\(a^{3} x+(a+1)^{3} y+(a+2)^{3} z=0 \\ a x+(a+1) y+(a+2) z=0 \\ x+y+z=0\)
has a non-zero solution is

79248 If \(\left[\begin{array}{lll}1 & 3 & 3 \\ 1 & 4 & 4 \\ 1 & 3 & 4\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}12 \\ 15 \\ 13\end{array}\right]\), then the value of \(x, y\), respectively are

79250 The system of linear equations \(x+y+z=2,2 x\) \(+y-z=3,3 x+2 y+k z=4\) has a unique solution if

79251 The system of equations \(k x+2 y-z=1,(k-1)\) \(y-2 z=2\) and \((k+2) z=3\) have a unique solution if \(k\) equals