Advertisements
Advertisements
प्रश्न
If A and B are square matrices of the same order, explain, why in general
(A + B)2 ≠ A2 + 2AB + B2
उत्तर
\[\left( i \right) LHS = \left( A + B \right)^2 \]
\[ = \left( A + B \right)\left( A + B \right)\]
\[ = A\left( A + B \right) + B\left( A + B \right)\]
\[ = A^2 + AB + BA + B^2\]
We know that a matrix does not have commutative property. So,
AB ≠ BA
Thus,
APPEARS IN
संबंधित प्रश्न
Which of the given values of x and y make the following pair of matrices equal?
`[(3x+7, 5),(y+1, 2-3x)] = [(0,y-2),(8,4)]`
Let `A = [(2,4),(3,2)] , B = [(1,3),(-2,5)], C = [(-2,5),(3,4)]`
Find BA
Compute the indicated products
`[(2,3,4),(3,4,5),(4,5,6)][(1,-3,5),(0,2,4), (3,0,5)]`
Compute the indicated product.
`[(3,-1,3),(-1,0,2)][(2,-3),(1,0),(3,1)]`
Compute the indicated products:
`[[a b],[-b a]][[a -b],[b a]]`
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]]`
Evaluate the following:
`[[1 -1],[0 2],[2 3]]` `([[1 0 2],[2 0 1]]-[[0 1 2],[1 0 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= `[[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.
\[A = \begin{bmatrix}3 & 1 \\ - 1 & 2\end{bmatrix} and \text{ I} = \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}\]
\[A = \begin{bmatrix}3 & 1 \\ - 1 & 2\end{bmatrix}\]show that A2 − 5A + 7I = O use this to find A4.
If
If A=, find k such that A2 = kA − 2I2
Find the value of x for which the matrix product`[[2 0 7],[0 1 0],[1 -2 1]]` `[[-x 14x 7x],[0 1 0],[x -4x -2x]]`equal an identity matrix.
Solve the matrix equations:
`[[],[x-5-1],[]][[1,0,2],[0,2,1],[2,0,3]] [[x],[4],[1]]=0`
Find the matrix A such that [2 1 3 ] `[[-1,0,-1],[-1,1,0],[0,1,1]] [[1],[0],[-1]]=A`
Find a 2 × 2 matrix A such that `A=[[1,-2],[1,4]]=6l_2`
If `A=[[0,0],[4,0]]` find `A^16`
Give examples of matrices
A and B such that AB ≠ BA
Let `A =[[2,-3],[-7,5]]` And `B=[[1,0],[2,-4]]` verify that
(A − B)T = AT − BT
Let `A =[[2,-3],[-7,5]]` And `B=[[1,0],[2,-4]]` 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 \[A = \begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ a & b & - 1\end{bmatrix}\] , then A2 is equal to ___________ .
The number of possible matrices of order 3 × 3 with each entry 2 or 0 is
If A and B are square matrices of the same order, then (A + B)(A − B) is equal to
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.
If A and B are square matrices of the same order, then (kA)′ = ______. (k is any scalar)
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 = `[(-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
