7. A manufacturer produces three products x, y, z which he sells in two markets. Annual sales are indicated below:
Market |
Products |
||
I |
10,000 |
2,000 |
18,000 |
II |
6,000 |
20,000 |
8,000 |
(a) If unit sale prices of x, y and z are Rs 2.50, Rs 1.50 and Rs 1.00, respectively, find the total revenue in each market with the help of matrix algebra.
(b) If the unit costs of the above three commodities are Rs 2.00, Rs 1.00 and 50 paise respectively. Find the gross profit.
Class 12
Matrices
Miscellaneous Exercise
1. If A and B are symmetric matrices, prove that AB–BA is a skew symmetric matrix.
5. If \(A=\begin{bmatrix}3&1 \\ -1&2\end{bmatrix}\), show that \(A^2-5A+7I=0\).
9. If \(A=\begin{bmatrix}α&β \\ γ &-α\end{bmatrix}\) is such that \(A^2=I\), then
(A) \(1+α^2+βγ=0\)
(B) \(1-α^2+βγ=0\)
(C) \(1-α^2-βγ=0\)
(D) \(1+α^2-βγ=0\).
10. If the matrix A is both symmetric and skew symmetric, then
(A) A is a diagonal matrix
(B) A is a zero matrix
(C) A is a square matrix
(D) None of these
11. If A is square matrix such that \(A^2=A\), then \((I+A)^3–7A\) is equal to
(A) A
(B) I–A
(C) I
(D) 3A