Advertisements
Advertisements
प्रश्न
If [1 1 x] `[[1 0 2],[0 2 1],[2 1 0]] [[1],[1],[1]]` = 0, find x.
उत्तर
Given : [1 1 x] `[[1,0,2],[0,2,1],[2,1 ,0]] [[1],[1],[1]]=0`
⇒[1+0+2x 0+2+x 2+1+0] `[[1],[1],[1]]=0`
⇒[1+2x 2+x 3] `[[1],[1],[1]]=0`
⇒[1+2x+2+x+3]=0
⇒6+3x=0
⇒3x=−6
⇒x=`(-6)/3`
∴ x=-2
APPEARS IN
संबंधित प्रश्न
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)]`
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]]`
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 A= `[[1 0 -2],[3 -1 0],[-2 1 1]]` B=,`[[0 5 -4],[-2 1 3],[-1 0 2]] and C=[[1 5 2],[-1 1 0],[0 -1 1]]` verify that A (B − C) = AB − AC.
\[A = \begin{bmatrix}2 & - 3 & - 5 \\ - 1 & 4 & 5 \\ 1 & - 3 & - 4\end{bmatrix}\] , Show that A2 = A.
If
If \[A = \begin{bmatrix}3 & - 5 \\ - 4 & 2\end{bmatrix}\] , find A2 − 5A − 14I.
Solve the matrix equations:
`[1 2 1] [[1,2,0],[2,0,1],[1,0 ,2]][[0],[2],[x]]=0`
If , then show that A is a root of the polynomial f (x) = x3 − 6x2 + 7x + 2.
\[A = \begin{bmatrix}\cos \alpha + \sin \alpha & \sqrt{2}\sin \alpha \\ - \sqrt{2}\sin \alpha & \cos \alpha - \sin \alpha\end{bmatrix}\] ,prove that
\[A^n = \begin{bmatrix}\text{cos n α} + \text{sin n α} & \sqrt{2}\text{sin n α} \\ - \sqrt{2}\text{sin n α} & \text{cos n α} - \text{sin n α} \end{bmatrix}\] for all n ∈ N.
Let A and B be square matrices of the same order. Does (A + B)2 = A2 + 2AB + B2 hold? If not, why?
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
The monthly incomes of Aryan and Babban are in the ratio 3 : 4 and their monthly expenditures are in the ratio 5 : 7. If each saves ₹ 15,000 per month, find their monthly incomes using matrix method. This problem reflects which value?
A trust invested some money in two type of bonds. The first bond pays 10% interest and second bond pays 12% interest. The trust received ₹ 2800 as interest. However, if trust had interchanged money in bonds, they would have got ₹ 100 less as interes. Using matrix method, find the amount invested by the trust.
Let `A =[[2,-3],[-7,5]]` And `B=[[1,0],[2,-4]]` verify that
(A − B)T = AT − BT
If `A=[[-2],[4],[5]]` , B = [1 3 −6], verify that (AB)T = BT AT
If \[A = \begin{bmatrix}1 & 1 \\ 1 & 1\end{bmatrix}\] satisfies A4 = λA, then write the value of λ.
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.
Construct a 2 × 2 matrix A = [aij] whose elements aij are given by \[a_{ij} = \begin{cases}\frac{\left| - 3i + j \right|}{2} & , if i \neq j \\ \left( i + j \right)^2 & , if i = j\end{cases}\]
If \[A = \begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ a & b & - 1\end{bmatrix}\] , then A2 is equal to ___________ .
If \[\begin{bmatrix}\cos\frac{2\pi}{7} & - \sin\frac{2\pi}{7} \\ \sin\frac{2\pi}{7} & \cos\frac{2\pi}{7}\end{bmatrix}^k = \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}\] then the least positive integral value of k is _____________.
If \[A = \begin{bmatrix}1 & a \\ 0 & 1\end{bmatrix}\]then An (where n ∈ N) equals
The matrix \[A = \begin{bmatrix}0 & 0 & 4 \\ 0 & 4 & 0 \\ 4 & 0 & 0\end{bmatrix}\] is a
If \[A = \begin{pmatrix}\cos\alpha & - \sin\alpha & 0 \\ \sin\alpha & \cos\alpha & 0 \\ 0 & 0 & 1\end{pmatrix},\] ,find adj·A and verify that A(adj·A) = (adj·A)A = |A| I3.
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'` .
Show that if A and B are square matrices such that AB = BA, then (A + B)2 = A2 + 2AB + B2.
Prove by Mathematical Induction that (A′)n = (An)′, where n ∈ N for any square matrix A.
If A and B are square matrices of the same order, then (AB)′ = ______.
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:
- What is the total amount of money collected by all three schools DPS, CVC, and KVS?
If A = `[(a, b),(b, a)]` and A2 = `[(α, β),(β, α)]`, then ______.
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
