Advertisements
Advertisements
प्रश्न
A trust fund has Rs 30000 that must be invested in two different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide Rs 30000 among the two types of bonds. If the trust fund must obtain an annual total interest of
(i) Rs 1800
उत्तर
If Rs x are invested in the first type of bond and Rs \[\left( 30000 - x \right)\]
are invested in the second type of bond, then the matrix
\[A = \begin{bmatrix}x & 30000 - x\end{bmatrix}\] represents investment and the matrix
B = \[\begin{bmatrix} \frac{5}{100} \\ \frac{7}{100} \end {bmatrix}\] represents rate of interest.
\[\left( i \right) \]
`[x 30000 - x ][[ 5/100],[7/100]] = [1800]`
`⇒ [(5x)/ 100 + "(7(30000-x))/100]= [1800]`
\[ \Rightarrow \frac{5x + 210000 - 7x}{100} = 1800\]
\[ \Rightarrow 210000 - 2x = 180000\]
\[ \Rightarrow 2x = 30000\]
\[ \Rightarrow x = 15000\]
\[\]
Thus,
Amount invested in the first bond = Rs 15000
Amount invested in the second bond = Rs\[\left( 30000 - 15000 \right)\] = 15000
APPEARS IN
संबंधित प्रश्न
Compute the indicated product.
`[(1),(2),(3)] [2,3,4]`
Compute the indicated products
`[(2,3,4),(3,4,5),(4,5,6)][(1,-3,5),(0,2,4), (3,0,5)]`
Compute the indicated product.
`[(3,-1,3),(-1,0,2)][(2,-3),(1,0),(3,1)]`
Compute the indicated products:
`[[a b],[-b a]][[a -b],[b a]]`
Show that AB ≠ BA in each of the following cases:
`A=[[1 3 0],[1 1 0],[4 1 0]]`And B=`[[0 1 0],[1 0 0],[0 5 1]]`
Compute the products AB and BA whichever exists in each of the following cases:
`A=[[3 2],[-1 0],[-1 1]]` and `B= [[4 5 6],[0 1 2]]`
Show that AB ≠ BA in each of the following cases:
`A = [[1,3,-1],[2,-1,-1],[3,0,-1]]` And `B= [[-2,3,-1],[-1,2,-1],[-6,9,-4]]`
If A = `[[2 -1],[3 2]]` and B = `[[0 4],[-1 7]]`find 3A2 − 2B + I
Let A =`[[-1 1 -1],[3 -3 3],[5 5 5]]`and B =`[[0 4 3],[1 -3 -3],[-1 4 4]]`
, compute A2 − B2.
For the following matrices verify the associativity of matrix multiplication i.e. (AB) C = A(BC):
`A=[[4 2 3],[1 1 2],[3 0 1]]`=`B=[[1 -1 1],[0 1 2],[2 -1 1]]` and `C= [[1 2 -1],[3 0 1],[0 0 1]]`
If [1 −1 x] `[[0 1 -1],[2 1 3],[1 1 1]] [[0],[1],[1]]=`= 0, find x.
If
If A=, find k such that A2 = kA − 2I2
Solve the matrix equations:
`[x1][[1,0],[-2,-3]][[x],[5]]=0`
If , then show that A is a root of the polynomial f (x) = x3 − 6x2 + 7x + 2.
Find the matrix A such that `=[[1,2,3],[4,5,6]]=[[-7,-8,-9],[2,4,6],[11,10,9]]`
If `A=[[0,0],[4,0]]` find `A^16`
`A=[[1,0,-3],[2,1,3],[0,1,1]]`then verify that A2 + A = A(A + I), where I is the identity matrix.
If B, C are n rowed square matrices and if A = B + C, BC = CB, C2 = O, then show that for every n ∈ N, An+1 = Bn (B + (n + 1) C).
Give examples of matrices
A and B such that AB = O but A ≠ 0, B ≠ 0.
If A and B are square matrices of the same order, explain, why in general
(A + B)2 ≠ A2 + 2AB + B2
Let A and B be square matrices of the order 3 × 3. Is (AB)2 = A2 B2? Give reasons.
If A and B are square matrices of the same order such that AB = BA, then show that (A + B)2 = A2 + 2AB + B2.
Let `A=[[1,1,1],[3,3,3]],B=[[3,1],[5,2],[-2,4]]` and `C=[[4,2],[-3,5],[5,0]]`Verify that AB = AC though B ≠ C, A ≠ O.
To promote making of toilets for women, an organisation tried to generate awarness through (i) house calls, (ii) letters, and (iii) announcements. The cost for each mode per attempt is given below:
(i) ₹50 (ii) ₹20 (iii) ₹40
The number of attempts made in three villages X, Y and Z are given below:
(i) (ii) (iii)
X 400 300 100
Y 300 250 75
Z 500 400 150
Find the total cost incurred by the organisation for three villages separately, using matrices.
Let `A =[[2,-3],[-7,5]]` And `B=[[1,0],[2,-4]]` verify that
(2A)T = 2AT
If A is an m × n matrix and B is n × p matrix does AB exist? If yes, write its order.
If A and B are two matrices such that AB = A and BA = B, then B2 is equal to
If A, B are square matrices of order 3, A is non-singular and AB = O, then B is a
If S = [Sij] is a scalar matrix such that sij = k and A is a square matrix of the same order, then AS = SA = ?
The matrix \[A = \begin{bmatrix}0 & 0 & 4 \\ 0 & 4 & 0 \\ 4 & 0 & 0\end{bmatrix}\] is a
If A = `[[3,9,0] ,[1,8,-2], [7,5,4]]` and B =`[[4,0,2],[7,1,4],[2,2,6]]` , then find the matrix `B'A'` .
If X = `[(3, 1, -1),(5, -2, -3)]` and Y = `[(2, 1, -1),(7, 2, 4)]`, find 2X – 3Y
Let A and B be square matrices of the order 3 × 3. Is (AB)2 = A2B2? Give reasons.
Show that if A and B are square matrices such that AB = BA, then (A + B)2 = A2 + 2AB + B2.
Let A = `[(1, 2),(-1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, -2)]` and a = 4, b = –2. Show that: A(BC) = (AB)C
If A = `[(0, 1),(1, 0)]`, then A2 is equal to ______.
If A and B are square matrices of the same order, then [k (A – B)]′ = ______.
Let a, b, c ∈ R be all non-zero and satisfy a3 + b3 + c3 = 2. If the matrix A = `((a, b, c),(b, c, a),(c, a, b))` satisfies ATA = I, then a value of abc can be ______.
