Science (English Medium) इयत्ता १२ - CBSE Question Bank Solutions for Mathematics

2x − y + z = 0
3x + 2y − z = 0
x + 4y + 3z = 0

2x − y + 2z = 0
5x + 3y − z = 0
x + 5y − 5z = 0

3x − y + 2z = 0
4x + 3y + 3z = 0
5x + 7y + 4z = 0

x + y − 6z = 0
x − y + 2z = 0
−3x + y + 2z = 0

x + y + z = 0
x − y − 5z = 0
x + 2y + 4z = 0

x + y − z = 0
x − 2y + z = 0
3x + 6y − 5z = 0

3x + y − 2z = 0
x + y + z = 0
x − 2y + z = 0

2x + 3y − z = 0
x − y − 2z = 0
3x + y + 3z = 0

If \[\begin{bmatrix}1 & 0 & 0 \\ 0 & - 1 & 0 \\ 0 & 0 & - 1\end{bmatrix}\begin{bmatrix}x \\ y \\ z\end{bmatrix} = \begin{bmatrix}1 \\ 0 \\ 1\end{bmatrix}\], find x, y and z.

If \[\begin{bmatrix}1 & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & 1\end{bmatrix}\begin{bmatrix}x \\ - 1 \\ z\end{bmatrix} = \begin{bmatrix}1 \\ 0 \\ 1\end{bmatrix}\] , find x, y and z.

Solve the following for x and y: \[\begin{bmatrix}3 & - 4 \\ 9 & 2\end{bmatrix}\binom{x}{y} = \binom{10}{ 2}\]

The system of equation x + y + z = 2, 3x − y + 2z = 6 and 3x + y + z = −18 has

The number of solutions of the system of equations
2x + y − z = 7
x − 3y + 2z = 1
x + 4y − 3z = 5
is

Let \[X = \begin{bmatrix}x_1 \\ x_2 \\ x_3\end{bmatrix}, A = \begin{bmatrix}1 & - 1 & 2 \\ 2 & 0 & 1 \\ 3 & 2 & 1\end{bmatrix}\text{ and }B = \begin{bmatrix}3 \\ 1 \\ 4\end{bmatrix}\] . If AX = B, then X is equal to

The number of solutions of the system of equations:
2x + y − z = 7
x − 3y + 2z = 1
x + 4y − 3z = 5

The system of linear equations:
x + y + z = 2
2x + y − z = 3
3x + 2y + kz = 4 has a unique solution if