Advertisements
Advertisements
प्रश्न
Compute the indicated product.
`[(2,1),(3,2),(-1,1)][(1,0,1),(-1,2,1)]`
उत्तर
`[(2,1),(3,2),(-1,1)][(1,0,1),(-1,2,1)]`
`= [(2(1)+1(-1), 2(0)+1(2), 2(1)+1(1)), (3(1)+2(-1), 3(0)+2(2), 3(1)+2(1)), (-1(1)+1(-1), -1(0)+1(2), -1(1)+1(1))]`
`= [(2-1,0+2, 2+1), (3-2,0+4, 3+2),(-1-1, 0+2,-1+1)]`
`= [(1,2,3),(1,4,5),(-2,2,0)]`
APPEARS IN
संबंधित प्रश्न
Let `A = [(2,4),(3,2)] , B = [(1,3),(-2,5)], C = [(-2,5),(3,4)]`
Find AB
Compute the indicated products:
`[[1 -2],[2 3]][[1 2 3],[-3 2 -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]]`
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]]`
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 = `[[2 -1],[3 2]]` and B = `[[0 4],[-1 7]]`find 3A2 − 2B + I
If A = `[[1 1],[0 1]]` show that A2 = `[[1 2],[0 1]]` and A3 = `[[1 3],[0 1]]`
\[A = \begin{bmatrix}2 & - 3 & - 5 \\ - 1 & 4 & 5 \\ 1 & - 3 & - 4\end{bmatrix}\] , Show that A2 = A.
\[A = \begin{bmatrix}3 & - 2 \\ 4 & - 2\end{bmatrix} and \text{ I }= \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}\], then prove that A2 − A + 2I = O.
If [1 1 x] `[[1 0 2],[0 2 1],[2 1 0]] [[1],[1],[1]]` = 0, find x.
If
If\[A = \begin{bmatrix}1 & 2 \\ 2 & 1\end{bmatrix}\] f (x) = x2 − 2x − 3, show that f (A) = 0
If `A= [[1,2,0],[3,-4,5],[0,-1,3]]` compute A2 − 4A + 3I3.
If f (x) = x2 − 2x, find f (A), where A=
Find a 2 × 2 matrix A such that `A=[[1,-2],[1,4]]=6l_2`
If `A=[[1,1],[0,1]] ,` Prove that `A=[[1,n],[0,1]]` for all positive integers n.
\[A = \begin{bmatrix}\cos \alpha + \sin \alpha & \sqrt{2}\sin \alpha \\ - \sqrt{2}\sin \alpha & \cos \alpha - \sin \alpha\end{bmatrix}\] ,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= [[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.
Let A and B be square matrices of the same order. Does (A + B)2 = A2 + 2AB + B2 hold? If not, why?
The cooperative stores of a particular school has 10 dozen physics books, 8 dozen chemistry books and 5 dozen mathematics books. Their selling prices are Rs. 8.30, Rs. 3.45 and Rs. 4.50 each respectively. Find the total amount the store will receive from selling all the items.
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
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.
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
If \[A = \begin{bmatrix}1 & 1 \\ 1 & 1\end{bmatrix}\] satisfies A4 = λA, then write the value of λ.
For any square matrix write whether AAT is symmetric or skew-symmetric.
If \[A = \begin{bmatrix}\cos \alpha & - \sin \alpha \\ \sin \alpha & \cos \alpha\end{bmatrix}\] is identity matrix, then write the value of α.
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 `A=[[i,0],[0,i ]]` , n ∈ N, then A4n equals
If \[A = \begin{bmatrix}1 & - 1 \\ 2 & - 1\end{bmatrix}, B = \begin{bmatrix}a & 1 \\ b & - 1\end{bmatrix}\]and (A + B)2 = A2 + B2, values of a and b are
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 X = `[(3, 1, -1),(5, -2, -3)]` and Y = `[(2, 1, -1),(7, 2, 4)]`, find X + Y
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.
If matrix A = [aij]2×2, where aij `{:(= 1 "if i" ≠ "j"),(= 0 "if i" = "j"):}` then A2 is equal to ______.
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?
