Advertisements
Advertisements
प्रश्न
If A, B and C are square matrices of same order, then AB = AC always implies that B = C
विकल्प
True
False
उत्तर
This statement is False.
Explanation:
Let A = `[(1, 0),(0, 0)]`
B = `[(0, 0),(2, 0)]`
And C = `[(0, 0),(3, 4)]`
∴ AB = `[(1, 0),(0, 0)] [(0, 0),(2, 0)] = [(0, 0),(0, 0)]`
AC = `[(1, 0),(0, 0)] [(0, 0),(3, 4)] = [(0, 0),(0, 0)]`
Here AB = AC = 0 but B ≠ C.
APPEARS IN
संबंधित प्रश्न
Compute the indicated products:
`[[1 -2],[2 3]][[1 2 3],[-3 2 -1]]`
Evaluate the following:
`([[1 3],[-1 -4]]+[[3 -2],[-1 1]])[[1 3 5],[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 = `[[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]]`
If A = `[[0,c,-b],[-c,0,a],[b,-a,0]]`and B =`[[a^2 ,ab,ac],[ab,b^2,bc],[ac,bc,c^2]]`, show that AB = BA = O3×3.
For the following matrices verify the distributivity of matrix multiplication over matrix addition i.e. A (B + C) = AB + AC:
`A = [[1 -1],[0 2]] B= [[-1 0],[2 1]]`and `C= [[0 1],[1 -1]]`
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]]`
If [1 −1 x] `[[0 1 -1],[2 1 3],[1 1 1]] [[0],[1],[1]]=`= 0, find x.
\[A = \begin{bmatrix}3 & 1 \\ - 1 & 2\end{bmatrix} and \text{ I} = \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}\]
`A=[[3,2, 0],[1,4,0],[0,0,5]]` show that A2 − 7A + 10I3 = 0
If\[A = \begin{bmatrix}a & b \\ 0 & 1\end{bmatrix}\], prove that\[A^n = \begin{bmatrix}a^n & b( a^n - 1)/a - 1 \\ 0 & 1\end{bmatrix}\] for every positive integer n .
If A and B are square matrices of the same order, explain, why in general
(A + B) (A − B) ≠ A2 − B2
Three shopkeepers A, B and C go to a store to buy stationary. A purchases 12 dozen notebooks, 5 dozen pens and 6 dozen pencils. B purchases 10 dozen notebooks, 6 dozen pens and 7 dozen pencils. C purchases 11 dozen notebooks, 13 dozen pens and 8 dozen pencils. A notebook costs 40 paise, a pen costs Rs. 1.25 and a pencil costs 35 paise. Use matrix multiplication to calculate each individual's bill.
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.
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.
If `A= [[3],[5],[2]]` And B=[1 0 4] , Verify that `(AB)^T=B^TA^T`
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.
Given an example of two non-zero 2 × 2 matrices A and B such that AB = O.
If \[A = \begin{bmatrix}- 3 & 0 \\ 0 & - 3\end{bmatrix}\] , find A4.
If A is a matrix of order 3 × 4 and B is a matrix of order 4 × 3, find the order of the matrix of AB.
If \[A = \begin{bmatrix}\cos \alpha & - \sin \alpha \\ \sin \alpha & \cos \alpha\end{bmatrix}\] is identity matrix, then write the value of α.
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 = `[(2, -1, 3),(-4, 5, 1)]` and B = `[(2, 3),(4, -2),(1, 5)]`, then ______.
If X = `[(3, 1, -1),(5, -2, -3)]` and Y = `[(2, 1, -1),(7, 2, 4)]`, find 2X – 3Y
Give an example of matrices A, B and C such that AB = AC, where A is nonzero matrix, but B ≠ C.
