Arts (English Medium) Class 12 - CBSE Question Bank Solutions

Two schools P and Q want to award their selected students on the values of Tolerance, Kindness and Leadership. The school P wants to award ₹x each, ₹y each and ₹z each for the three respective values to 3, 2 and 1 students respectively with a total award money of ₹2,200. School Q wants to spend ₹3,100 to award its 4, 1 and 3 students on the respective values (by giving the same award money to the three values as school P). If the total amount of award for one prize on each values is ₹1,200, using matrices, find the award money for each value.
Apart from these three values, suggest one more value which should be considered for award.

A total amount of ₹7000 is deposited in three different saving bank accounts with annual interest rates 5%, 8% and \[8\frac{1}{2}\] % respectively. The total annual interest from these three accounts is ₹550. Equal amounts have been deposited in the 5% and 8% saving accounts. Find the amount deposited in each of the three accounts, with the help of matrices.

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