Advertisements
Advertisements
Question
If A = `[(1, 2),(4, 1),(5, 6)]` B = `[(1, 2),(6, 4),(7, 3)]`, then verify that: (2A + B)′ = 2A′ + B′
Advertisements
Solution
Given that: A = `[(1, 2),(4, 1),(5, 6)]` and B = `[(1, 2),(6, 4),(7, 3)]`
L.H.S. (2A + B)' = `[2((1, 2),(4, 1),(5, 6)) + ((1, 2),(6, 4),(7, 3))]^'`
= `[((2, 4),(8, 2),(10, 12)) + ((1, 2),(6, 4),(7, 3))]^'`
= `[(2 + 1, 4 + 2),(8 + 6, 2 + 4),(10 + 7, 12 + 3)]^'`
= `[(3, 6),(14, 6),(17, 15)]^'`
= `[(3, 14, 17),(6, 6, 15)]`
R.H.S. 2A' + B' = `2[(1, 2),(4, 1),(5, 6)]^' + [(1, 2),(6, 4),(7, 3)]^'`
= `2[(1, 4, 5),(2, 1, 6)] + [(1, 6, 7),(2, 4, 3)]`
= `[(2, 8, 10),(4, 2, 12)] + [(1, 6, 7),(2, 4, 3)]`
= `[(2 + 1, 8 + 6, 10 + 7),(4 + 2, 2 + 4, 12 + 3)]`
= `[(3, 14, 17),(6, 6, 15)]`
Hence, L.H.S. = R.H.S.
(2A + B)′ = 2A′ + B′ is verified.
APPEARS IN
RELATED QUESTIONS
if `A=[[2,0,0],[0,2,0],[0,0,2]]` then A6= ......................
If A = `([cos alpha, sin alpha],[-sinalpha, cos alpha])` , find α satisfying 0 < α < `pi/r`when `A+A^T=sqrt2I_2` where AT is transpose of A.
If `A=([2,0,1],[2,1,3],[1,-1,0])` find A2 - 5A + 4I and hence find a matrix X such that A2 - 5A + 4I + X = 0
Let `A = [(2,4),(3,2)] , B = [(1,3),(-2,5)], C = [(-2,5),(3,4)]`
Find A + B
Compute the following:
`[(a,b),(-b, a)] + [(a,b),(b,a)]`
Compute the following:
`[(a^2+b^2, b^2+c^2),(a^2+c^2, a^2+b^2)] + [(2ab , 2bc),(-2ac, -2ab)]`
Compute the following:
`[(-1,4, -6),(8,5,16),(2,8,5)] + [(12,7,6),(8,0,5),(3,2,4)]`
Compute the following:
`[(cos^2x, sin^2 x),(sin^2 x ,cos^2 x)]+[(sin^2 x, cos^2 x), (cos^2 x, sin^2 x)]`
Compute the following sums:
`[[3 -2],[1 4]]+ [[-2 4 ],[1 3]]`
Let A = `[[2,4],[3,2]]`, `B=[[1,3],[-2,5]]`and `c =[[-2,5],[3,4]]`.Find each of the following: 2A − 3B
Let A = `[[2,4],[3,2]]`, `B=[[1,3],[-2,5]]`and `c =[[-2,5],[3,4]]`.Find each of the following: B − 4C
If A =`[[2,3],[5,7]],B =` `[[-1,0 ,2],[3,4,1]]`,`C= [[-1,2,3],[2,1,0]]`find : A + B and B + C
If A =`[[2 3],[5 7]],B =` `[[-1 0 2],[3 4 1]]`,`C= [[-1 2 3],[2 1 0]]`find
2B + 3A and 3C − 4B
Let A = `[[-1 0 2],[3 1 4]]``B=[[0 -2 5],[1 -3 1]]``and C = [[1 -5 2],[6 0 -4 ]]`Compute2A2-3B +4C :
If A = diag (2 − 59), B = diag (11 − 4) and C = diag (−6 3 4), find
B + C − 2A
If A = diag (2 − 59), B = diag (11 − 4) and C = diag (−6 3 4), find
2A + 3B − 5C
If A = `[[2 -2],[4 2],[-5 1]],B=[[8 0],[4 -2],[3 6]]`
, find matrix X such that 2A + 3X = 5B.
If A = `[[1 -3 2],[2 0 2]]`and `B = [[2 -1 -1],[1 0 -1]]` find the matrix C such that A + B + C is
, find the matrix C such that A + B + C is zero matrix.
Find x, y satisfying the matrix equations
`[[X-Y 2 -2],[4 x 6]]+[[3 -2 2],[1 0 -1]]=[[ 6 0 0],[ 5 2x+y 5]]`
Find x, y satisfying the matrix equations
`[x y + 2 z-3 ] + [ y 4 5]=[4 9 12]`
Find x, y satisfying the matrix equations
`x[[2],[1]]+y[[3],[5]]+[[-8],[-11]]=0`
If 2 `[[3 4],[5 x]]+[[1 y],[0 1]]=[[7 0],[10 5]]` find x and y.
Find a matrix X such that 2A + B + X = O, where
`A= [[-1 2],[3 4]],B= [[3 -2],[1 5]]`
Find x, y, z and t, if
`2[[x 5],[z t]]+[[x 6],[-1 2t]]=[[7 14],[15 14]]`
If w is a complex cube root of unity, show that
`([[1 w w^2],[w w^2 1],[w^2 1 w]]+[[w w^2 1],[w^2 1 w],[w w^2 1]])[[1],[w],[w^2]]=[[0],[0],[0]]`
If \[A = \begin{bmatrix}\cos x & \sin x \\ - \sin x & \cos x\end{bmatrix}\] , find x satisfying 0 < x < \[\frac{\pi}{2}\] when A + AT = I
If A = [aij] is a skew-symmetric matrix, then write the value of \[\sum_i \sum_j\] aij.
Find the values of x and y, if \[2\begin{bmatrix}1 & 3 \\ 0 & x\end{bmatrix} + \begin{bmatrix}y & 0 \\ 1 & 2\end{bmatrix} = \begin{bmatrix}5 & 6 \\ 1 & 8\end{bmatrix}\]
If \[x\binom{2}{3} + y\binom{ - 1}{1} = \binom{10}{5}\] , find the value of x.
If \[\binom{x + y}{x - y} = \begin{bmatrix}2 & 1 \\ 4 & 3\end{bmatrix}\binom{1}{ - 2}\] , then write the value of (x, y).
If \[I = \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}, J = \begin{bmatrix}0 & 1 \\ - 1 & 0\end{bmatrix} and B = \begin{bmatrix}\cos \theta & \sin \theta \\ - \sin \theta & \cos \theta\end{bmatrix}\] then B equals )
The trace of the matrix \[A = \begin{bmatrix}1 & - 5 & 7 \\ 0 & 7 & 9 \\ 11 & 8 & 9\end{bmatrix}\], is
Addition of matrices is defined if order of the matrices is ______.
If possible, find the sum of the matrices A and B, where A = `[(sqrt(3), 1),(2, 3)]`, and B = `[(x, y, z),(a, "b", 6)]`
If A = `[(2, 1)]`, B = `[(5, 3, 4),(8, 7, 6)]` and C = `[(-1, 2, 1),(1, 0, 2)]`, verify that A(B + C) = (AB + AC).
Let A = `[(1, 2),(-1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, -2)]` and a = 4, b = –2. Show that: A + (B + C) = (A + B) + C
Let A = `[(1, 2),(-1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, -2)]` and a = 4, b = –2. Show that: (a + b)B = aB + bB
If A = `[(1, 2),(4, 1)]`, find A2 + 2A + 7I.
Matrix multiplication is ______ over addition.
Matrices of any order can be added.
`"A" = [(1,-1),(2,-1)], "B" = [("x", 1),("y", -1)]` and (A + B)2 = A2 + B2, then x + y = ____________.
If `[(2"a"+"b", "a"-2"b"),(5"c" - "d", 4"c"+3"d")] = [(4, -3),(11, 24)]`, then value of a + b – c + 2d is:
If A `= [(0,2),(2,0)],` then A2 is ____________.
If a2 + b2 + c2 = –2 and f(x) = `|(1 + a^2x, (1 + b^2)x, (1 + c^2)x),((1 + a^2)x, 1 + b^2x, (1 + c^2)x),((1 + a^2)x, (1 + b^2)x, (1 + c^2)x)|` then f(x) is a polynomial of degree ______.
