Advertisements
Advertisements
Question
The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling prices are Rs 80, Rs 60 and Rs 40 each respectively. Find the total amount the bookshop will receive from selling all the books using matrix algebra.
Advertisements
Solution
The number of books in the school is as follows:
Chemistry: 10 dozen = 120 books
Physics: 8 dozen = 96 books
Economics: 10 dozen = 120 books
This can be expressed as matrix A = [120 96 120].
The selling price of each book of Chemistry, Physics and Economics is Rs 80, Rs 60 and Rs 40, respectively.
This can be expressed as matrix R = `[(80),(60),(40)]`.
∴ Amount received, AR = `[120 96 120] [(80),(60),(40)]`
= 120 × 80 + 96 × 60 + 120 × 40
= [9600 + 5760 + 4800]
= [20,160]
So, the total amount received = Rs 20,160.
APPEARS IN
RELATED QUESTIONS
State, whether the following statement is true or false. If false, give a reason.
If A and B are two matrices of orders 3 × 2 and 2 × 3 respectively; then their sum A + B is possible.
State, whether the following statement is true or false. If false, give a reason.
Transpose of a square matrix is a square matrix.
Solve for a, b and c; if `[(a, a - b),(b + c, 0)] = [(3, -1),(2, 0)]`
If `A = [(2),(5)], B = [(1),(4)]` and `C = [(6),(-2)]`, find A + B – C
Given : M = `[(5, -3),(-2, 4)]`, find its transpose matrix Mt. If possible, find M + Mt
Given : M = `[(5, -3),(-2, 4)]`, find its transpose matrix Mt. If possible, find Mt – M
Evaluate:
`2[(-1 0)/(2 -3)] +[(3 3)/(5 0)]`
State, with reason, whether the following is true or false. A, B and C are matrices of order 2 × 2.
A – B = B – A
State, with reason, whether the following is true or false. A, B and C are matrices of order 2 × 2.
(B . C) . A = B . (C . A)
State, with reason, whether the following is true or false. A, B and C are matrices of order 2 × 2.
A . (B – C) = A . B – A . C
State, with reason, whether the following is true or false. A, B and C are matrices of order 2 × 2.
A2 – B2 = (A + B) (A – B)
State, with reason, whether the following is true or false. A, B and C are matrices of order 2 × 2.
(A – B)2 = A2 – 2A . B + B2
If M = `[(2,1),(1,-2)] `; find M2, M3 and M5.
Solve the following system of linear equation using matrix method:
`1/x + 1/y +1/z = 9`
`2/x + 5/y+7/z = 52`
`2/x+1/y-1/z=0`
Classify the following matrix :
`[(7, 0)]`
Classify the following matrix :
`|(11 , 3 , 0),(21 , 8 , 4),(15,5,2)|`
Find the values of a, b, c and d, if `|("a + 3b", 3"c" + "d"),(2"a" - "b" , "c" - 2"d")| = |(5 , 8),(3 , 5)|`
If A = `|(1,9,4),(5 , 0 , 3)|` find A'
If B = `|(15 , 13),(11,12),(10,17)|` , find the transpose of matrix Band If possible find the sum of the two matrices. If not possible state the reason.
If A = `|(5,"r"),("p",7)|` , c and if A + B = (9,7),(5,8) , find the values of p,q,r and s.
Evaluate the following :
`|(0 , 1),(-1 , 2),(-2 , 0)| |(0 , -4 , 0),(3 , 0 , -1)|`
Let A = `|(3 , 2),(0 ,5)|` and B = `|(1 ,0),(1 ,2)|` , find (i) (A + B)(A - B) (ii) A2 - B2 . Is (i) equal to (ii) ?
If A = `[(2, 3), (1, 2)], B = [(1, 0),(3, 1)]`, Find (AB)-1
Write the negation of the following statements :
(a) Radha likes tea or coffee.
(b) `∃x cc` R such that x + 3 ≥ 10.
If A = `[(1,2), (1,3)]`, find A2 - 3A
Solve the equation x + y = 4 and 2x - y = 5 using the method of reduction.
Find the adjoint of the matrix `"A" = [(2,-3),(3,5)]`
Solve the following minimal assignment problem :
| Machines | Jobs | ||
| I | II | III | |
| M1 | 1 | 4 | 5 |
| M2 | 4 | 2 | 7 |
| M3 | 7 | 8 | 3 |
Using the truth table statement, examine whether the statement pattern (p → q) ↔ (∼ p v q) is a tautology, a contradiction or a contingency.
`[(2, -1),(5, 1)]`
`[(2 , 7, 8),(-1 , sqrt(2), 0)]`
`[(0, 0, 0),(0, 0, 0)]`
Given `[(2, 1),(-3, 4)], "X" = [(7),(6)]` the order of the matrix X
Choose the correct answer from the given four options :
If A = [aij]2×2 where aij = i + j, then A is equal to
Construct a matrix A = [aij]3 × 2 whose element aij is given by
aij = i – 3j
The construction of demand line or supply line is the result of using
If `M xx [(3, 2),(-1, 0)] = [(3, -1)]`, the order of matrix M is ______.
