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प्रश्न
If A and B are square matrices of the same order, then (kA)′ = ______. (k is any scalar)
उत्तर
If A and B are square matrices of the same order, then (kA)′ = kA'. (k is any scalar)
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संबंधित प्रश्न
Compute the indicated product.
`[(1),(2),(3)] [2,3,4]`
Compute the indicated product.
`[(2,1),(3,2),(-1,1)][(1,0,1),(-1,2,1)]`
Compute the indicated products:
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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 = `[[1 1],[0 1]]` show that A2 = `[[1 2],[0 1]]` and A3 = `[[1 3],[0 1]]`
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If A =`[[2 -3 -5],[-1 4 5],[1 -3 -4]]` and B =`[[2 -2 -4],[-1 3 4],[1 2 -3]]`
, show that AB = A and BA = B.
If [x 4 1] `[[2 1 2],[1 0 2],[0 2 -4]]` `[[x],[4],[-1]]` = 0, find x.
\[A = \begin{bmatrix}3 & - 2 \\ 4 & - 2\end{bmatrix} and \text{ I }= \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}\], then prove that A2 − A + 2I = O.
Solve the matrix equations:
`[1 2 1] [[1,2,0],[2,0,1],[1,0 ,2]][[0],[2],[x]]=0`
`A=[[3,-5],[-4,2]]` then find A2 − 5A − 14I. Hence, obtain A3
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If A and B are square matrices of the same order such that AB = BA, then show that (A + B)2 = A2 + 2AB + B2.
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(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.
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.
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write AB.
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If A = [aij] is a square matrix such that aij = i2 − j2, then write whether A is symmetric or skew-symmetric.
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 AB = A and BA = B, where A and B are square matrices, then
If \[\begin{bmatrix}2x + y & 4x \\ 5x - 7 & 4x\end{bmatrix} = \begin{bmatrix}7 & 7y - 13 \\ y & x + 6\end{bmatrix}\]
If A = `[(0, 1),(1, 0)]`, then A2 is equal to ______.
If matrix A = [aij]2×2, where aij `{:(= 1 "if i" ≠ "j"),(= 0 "if i" = "j"):}` then A2 is equal to ______.
If A and B are square matrices of the same order, then [k (A – B)]′ = ______.
