Advertisements
Advertisements
प्रश्न
Solve the matrix equations:
`[[],[x-5-1],[]][[1,0,2],[0,2,1],[2,0,3]] [[x],[4],[1]]=0`
उत्तर
`[[],[x-5-1],[]][[1 0 2],[0 2 1],[2 0 3]] [[x],[4],[1]]=0`
⇒[x−0−2 0−10−0 2x−5−3] `[[x],[4],[1]]=0`
⇒[x−2 −10 2x−8 ] `[[x],[4],[1]]=0`
⇒[x2−2x−40+2x−8]=0
⇒x2−48=0
⇒x2=48
`⇒ x= ± sqrt48`
APPEARS IN
संबंधित प्रश्न
Compute the indicated product.
`[(1, -2),(2,3)][(1,2,3),(2,3,1)]`
Compute the products AB and BA whichever exists in each of the following cases:
`A= [[1 -2],[2 3]]` and B=`[[1 2 3],[2 3 1]]`
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 = `[[4 2],[-1 1]]`
, prove that (A − 2I) (A − 3I) = O
If A =
\[\begin{bmatrix}2 & - 3 & - 5 \\ - 1 & 4 & 5 \\ 1 & - 3 & - 4\end{bmatrix}\]and B =
\[\begin{bmatrix}- 1 & 3 & 5 \\ 1 & - 3 & - 5 \\ - 1 & 3 & 5\end{bmatrix}\] , show that AB = BA = O3×3.
If A = `[[0,c,-b],[-c,0,a],[b,-a,0]]`and B =`[[a^2 ,ab,ac],[ab,b^2,bc],[ac,bc,c^2]]`, show that AB = BA = O3×3.
For the following matrices verify the distributivity of matrix multiplication over matrix addition i.e. A (B + C) = AB + AC:
`A=[[2 -1],[1 1],[-1 2]]` `B=[[0 1],[1 1]]` C=`[[1 -1],[0 1]]`
Solve the matrix equations:
`[x1][[1,0],[-2,-3]][[x],[5]]=0`
`A=[[1,2,2],[2,1,2],[2,2,1]]`, then prove that A2 − 4A − 5I = 0
`A=[[3,-5],[-4,2]]` then find A2 − 5A − 14I. Hence, obtain A3
Let `A= [[1,1,1],[0,1,1],[0,0,1]]` Use the principle of mathematical introduction to show that `A^n [[1,n,n(n+1)//2],[0,1,1],[0,0,1]]` for every position integer n.
Give examples of matrices
A and B such that AB ≠ BA
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, explain, why in general
(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.
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(ii) Rs 2000
Let `A =[[2,-3],[-7,5]]` And `B=[[1,0],[2,-4]]` verify that
(AB)T = BT AT
Let `A= [[1,-1,0],[2,1,3],[1,2,1]]` And `B=[[1,2,3],[2,1,3],[0,1,1]]` Find `A^T,B^T` and verify that (A + B)T = AT + BT
If A is an m × n matrix and B is n × p matrix does AB exist? If yes, write its order.
Given an example of two non-zero 2 × 2 matrices A and B such that AB = O.
Write matrix A satisfying ` A+[[2 3],[-1 4]] =[[3 6],[- 3 8]]`.
For any square matrix write whether AAT is symmetric or skew-symmetric.
Write a 2 × 2 matrix which is both symmetric and skew-symmetric.
If `[2 1 3]([-1,0,-1],[-1,1,0],[0,1,1])([1],[0],[-1])=A` , then write the order of matrix A.
If \[A = \begin{bmatrix}1 & 2 & x \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix} and B = \begin{bmatrix}1 & - 2 & y \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}\] and AB = I3, then x + y equals
The matrix \[A = \begin{bmatrix}0 & 0 & 4 \\ 0 & 4 & 0 \\ 4 & 0 & 0\end{bmatrix}\] is a
If X = `[(3, 1, -1),(5, -2, -3)]` and Y = `[(2, 1, -1),(7, 2, 4)]`, find 2X – 3Y
If AB = BA for any two square matrices, prove by mathematical induction that (AB)n = AnBn
If A `= [(1,-2,1),(2,1,3)]` and B `= [(2,1),(3,2),(1,1)],` then (AB)T is equal
Three schools DPS, CVC, and KVS decided to organize a fair for collecting money for helping the flood victims. They sold handmade fans, mats, and plates from recycled material at a cost of Rs. 25, Rs.100, and Rs. 50 each respectively. The numbers of articles sold are given as
| School/Article | DPS | CVC | KVS |
| Handmade/fans | 40 | 25 | 35 |
| Mats | 50 | 40 | 50 |
| Plates | 20 | 30 | 40 |
Based on the information given above, answer the following questions:
- What is the total amount of money collected by all three schools DPS, CVC, and KVS?
Three schools DPS, CVC, and KVS decided to organize a fair for collecting money for helping the flood victims. They sold handmade fans, mats, and plates from recycled material at a cost of Rs. 25, Rs.100, and Rs. 50 each respectively. The numbers of articles sold are given as
| School/Article | DPS | CVC | KVS |
| Handmade/fans | 40 | 25 | 35 |
| Mats | 50 | 40 | 50 |
| Plates | 20 | 30 | 40 |
Based on the information given above, answer the following questions:
- How many articles (in total) are sold by three schools?
