Advertisements
Advertisements
Question
Solution
\[Given: \hspace{0.167em} A = \begin{bmatrix}5 & 2 & x \\ y & z & - 3 \\ 4 & t & - 7\end{bmatrix}\]
\[ \Rightarrow A^T = \begin{bmatrix}5 & y & 4 \\ 2 & z & t \\ x & - 3 & - 7\end{bmatrix}\]
Since A is a symmetric matrix,`( A^T)` = A .
\[ \Rightarrow \begin{bmatrix}5 & y & 4 \\ 2 & z & t \\ x & - 3 & - 7\end{bmatrix} = \begin{bmatrix}5 & 2 & x \\ y & z & - 3 \\ 4 & t & - 7\end{bmatrix}\]
The corresponding elements of two equal matrices are equal .
\[ \therefore x = 4 \]
\[ y = 2 \]
\[ z = z \]
\[ t = - 3\]
APPEARS IN
RELATED QUESTIONS
Let `A = [(2,4),(3,2)] , B = [(1,3),(-2,5)], C = [(-2,5),(3,4)]`
Find BA
Compute the indicated product:
`[(a,b),(-b,a)][(a,-b),(b,a)]`
Compute the indicated product.
`[(2,1),(3,2),(-1,1)][(1,0,1),(-1,2,1)]`
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 2,000.
Compute the indicated products:
`[[a b],[-b a]][[a -b],[b a]]`
Compute the indicated product:
`[(2,3,4),(3,4,5),(4,5,6)][(1,-3,5),(0,2,4), (3,0,5)]`
Show that AB ≠ BA in each of the following cases:
`A= [[5 -1],[6 7]]`And B =`[[2 1],[3 4]]`
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]]`
Compute the products AB and BA whichever exists in each of the following cases:
A = [1 −1 2 3] and B=`[[0],[1],[3],[2]]`
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]]`
\[A = \begin{bmatrix}3 & 1 \\ - 1 & 2\end{bmatrix} and \text{ I} = \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}\]
If
If `[[2 3],[5 7]] [[1 -3],[-2 4]]-[[-4 6],[-9 x]]` find x.
Solve the matrix equations:
`[x1][[1,0],[-2,-3]][[x],[5]]=0`
Solve the matrix equations:
`[[],[x-5-1],[]][[1,0,2],[0,2,1],[2,0,3]] [[x],[4],[1]]=0`
If f (x) = x2 − 2x, find f (A), where A=
`A=[[2,0,1],[2,1,3],[1,-1,0]]` , find A2 − 5A + 4I and hence find a matrix X such that A2 − 5A + 4I + X = 0.
Give examples of matrices
A, B and C such that AB = AC but B ≠ C, A ≠ 0.
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, explain, why in general
(A − B)2 ≠ A2 − 2AB + B2
In a legislative assembly election, a political group hired a public relations firm to promote its candidates in three ways: telephone, house calls and letters. The cost per contact (in paise) is given matrix A as
Cost per contact
`A=[[40],[100],[50]]` `[["Teliphone"] ,["House call "],[" letter"]]`
The number of contacts of each type made in two cities X and Y is given in matrix B as
Telephone House call Letter
`B= [[ 1000, 500, 5000],[3000,1000, 10000 ]]`
Find the total amount spent by the group in the two cities X and Y.
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 (2A)T = 2AT.
If `A=[[-2],[4],[5]]` , B = [1 3 −6], verify that (AB)T = BT AT
If A is an m × n matrix and B is n × p matrix does AB exist? If yes, write its order.
Write the number of all possible matrices of order 2 × 2 with each entry 1, 2 or 3.
If `A=[[i,0],[0,i ]]` , n ∈ N, then A4n equals
If A, B are square matrices of order 3, A is non-singular and AB = O, then B is a
The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is
If A = [aij] is a scalar matrix of order n × n such that aii = k, for all i, then trace of A is equal to
(a) nk (b) n + k (c) \[\frac{n}{k}\] (d) none of these
If \[\begin{bmatrix}2x + y & 4x \\ 5x - 7 & 4x\end{bmatrix} = \begin{bmatrix}7 & 7y - 13 \\ y & x + 6\end{bmatrix}\]
Give an example of matrices A, B and C such that AB = AC, where A is nonzero matrix, but B ≠ C.
If A and B are square matrices of the same order, then [k (A – B)]′ = ______.
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:
- How many articles (in total) are sold by three schools?
If A = `[(a, b),(b, a)]` and A2 = `[(α, β),(β, α)]`, then ______.
