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 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]]`
Evaluate the following:
`[[],[1 2 3],[]]` `[[1 0 2],[2 0 1],[0 1 2]]` `[[2],[4],[6]]`
If A = `[[1 0],[0 1]]`,B`[[1 0],[0 -1]]`
and C= `[[0 1],[1 0]]`
, then show that A2 = B2 = C2 = I2.
If A = `[[ cos 2θ sin 2θ],[ -sin 2θ cos 2θ]]`, find A2.
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.
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]]`
For the following matrices verify the distributivity of matrix multiplication over matrix addition i.e. A (B + C) = AB + AC:
`A = [[1 -1],[0 2]] B= [[-1 0],[2 1]]`and `C= [[0 1],[1 -1]]`
Compute the elements a43 and a22 of the matrix:`A=[[0 1 0],[2 0 2],[0 3 2],[4 0 4]]` `[[2 -1],[-3 2],[4 3]] [[0 1 -1 2 -2],[3 -3 4 -4 0]]`
\[A = \begin{bmatrix}3 & 1 \\ - 1 & 2\end{bmatrix} and \text{ I} = \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}\]
Show that the matrix \[A = \begin{bmatrix}5 & 3 \\ 12 & 7\end{bmatrix}\] is root of the equation A2 − 12A − I = O
If [1 1 x] `[[1 0 2],[0 2 1],[2 1 0]] [[1],[1],[1]]` = 0, find x.
If\[A = \begin{bmatrix}1 & 2 \\ 2 & 1\end{bmatrix}\] f (x) = x2 − 2x − 3, show that f (A) = 0
If f (x) = x2 − 2x, find f (A), where A=
Find the matrix A such that `=[[1,2,3],[4,5,6]]=[[-7,-8,-9],[2,4,6],[11,10,9]]`
Find a 2 × 2 matrix A such that `A=[[1,-2],[1,4]]=6l_2`
Let A and B be square matrices of the same order. Does (A + B)2 = A2 + 2AB + B2 hold? If not, why?
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.
There are 2 families A and B. There are 4 men, 6 women and 2 children in family A, and 2 men, 2 women and 4 children in family B. The recommend daily amount of calories is 2400 for men, 1900 for women, 1800 for children and 45 grams of proteins for men, 55 grams for women and 33 grams for children. Represent the above information using matrix. Using matrix multiplication, calculate the total requirement of calories and proteins for each of the two families. What awareness can you create among people about the planned diet from this question?
Let `A =[[2,-3],[-7,5]]` And `B=[[1,0],[2,-4]]` verify that
(A + B)T = AT + BT
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=[[-2],[4],[5]]` , B = [1 3 −6], verify that (AB)T = BT AT
If \[A = \begin{bmatrix}\cos x & - \sin x \\ \sin x & \cos x\end{bmatrix}\] , find AAT
Write matrix A satisfying ` A+[[2 3],[-1 4]] =[[3 6],[- 3 8]]`.
If I is the identity matrix and A is a square matrix such that A2 = A, then what is the value of (I + A)2 = 3A?
If A is a square matrix such that A2 = A, then write the value of 7A − (I + A)3, where I is the identity matrix.
If A and B are two matrices such that AB = A and BA = B, then B2 is equal to
If A is a matrix of order m × n and B is a matrix such that ABT and BTA are both defined, then the order of matrix B is
Disclaimer: option (a) and (d) both are the same.
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'` .
Prove by Mathematical Induction that (A′)n = (An)′, where n ∈ N for any square matrix A.
If A and B are two square matrices of the same order, then AB = BA.
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:
- If the number of handmade fans and plates are interchanged for all the schools, then what is the total money collected by all schools?
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?
A trust fund has Rs. 30,000 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 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of Rs. 1,800.
If A = `[(-3, -2, -4),(2, 1, 2),(2, 1, 3)]`, B = `[(1, 2, 0),(-2, -1, -2),(0, -1, 1)]` then find AB and use it to solve the following system of equations:
x – 2y = 3
2x – y – z = 2
–2y + z = 3