List of top Mathematics Questions on Determinants asked in UP Board XII

Solve the system of linear equations by Matrix Method: \(2x-3y+5z=11\), \(3x+2y-4z=-5\), \(x+y-2z=-3\).

Solve by matrix method the system of equations: \(x-y+2z=7,\ 3x+4y-5z=-5,\ 2x-y+3z=12\).

Find the value of the determinant \(\begin{vmatrix}17&15&13\\9&-8&7\\-3&2&5\end{vmatrix}\).

Find the value of the determinant \(\begin{vmatrix}a&b&c\\a^2&b^2&c^2\\a^3&b^3&c^3\end{vmatrix}\).

Find the value of the determinant \(\begin{vmatrix}x&a&x+a\\y&b&y+b\\z&c&z+c\end{vmatrix}\).

Solve the system of linear equations by Matrix Method: \(2x+3y+3z=5\), \(x-2y+z=-4\), \(3x-y-2z=3\).

Find the value of the determinant \(\begin{vmatrix}18&22&-13\\7&-9&11\\-11&7&17\end{vmatrix}\).

Solve the following system of equations by matrix method: \(\dfrac2x+\dfrac3y+\dfrac{10}z=4\), \(\dfrac4x-\dfrac6y+\dfrac5z=1\), \(\dfrac6x+\dfrac9y-\dfrac{20}z=2\).

Find the value of the determinant \(\begin{vmatrix}a & b & c\\ b & c & a\\ c & a & b\end{vmatrix}\).