Advertisements
Advertisements
प्रश्न
Let A = `[[2,4],[3,2]]`, `B=[[1,3],[-2,5]]`and `c =[[-2,5],[3,4]]`.Find each of the following: 2A − 3B
उत्तर
2A−3B
⇒ 2A - 3B =` 2[[2 4],[3 2 ]]`-3`[[1 3],[-2 5]]`
⇒ 2A−3B=`[[4 8],[6 4]]-[[1 3],[-2 5]]`
⇒ 2A−3B= `[[4 8],[6 4]]-[[3 9],[-6 15]]`
⇒ 2A−3B=`[[4 -3 8-9],[6+6 4-15]]`
⇒ 2A−3B=`[[1 -1],[12 -11]]`
APPEARS IN
संबंधित प्रश्न
if `A=[[2,0,0],[0,2,0],[0,0,2]]` then A6= ......................
Solve the following matrix equation for x: `[x 1] [[1,0],[−2,0]]=0`
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=[[1,2,2],[2,1,2],[2,2,1]]` ,then show that `A^2-4A-5I=0` and hence find A-1.
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: 3A − C
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
Find matrices X and Y, if 2X − Y = `[[6 -6 0],[-4 2 1]]`and X + 2Y =`[[3 2 5],[-2 1 -7 ]]`
If A = `[[2 -2],[4 2],[-5 1]],B=[[8 0],[4 -2],[3 6]]`
, find matrix X such that 2A + 3X = 5B.
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]`
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
`3[[x y],[z t]]=[[x 6],[-1 2t]]+[[4 x+y],[z+t 3]]`
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 \[2\begin{bmatrix}3 & 4 \\ 5 & x\end{bmatrix} + \begin{bmatrix}1 & y \\ 0 & 1\end{bmatrix} = \begin{bmatrix}7 & 0 \\ 10 & 5\end{bmatrix}\] , find 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
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 = `[(1, 2),(-2, 1)]`, B = `[(2, 3),(3, -4)]` and C = `[(1, 0),(-1, 0)]`, verify: A(B + C) = AB + AC
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).
If A = `[(1, 2),(4, 1),(5, 6)]` B = `[(1, 2),(6, 4),(7, 3)]`, then verify that: (2A + B)′ = 2A′ + B′
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
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:
Let A = `[(1, -1),(2, α)]` and B = `[(β, 1),(1, 0)]`, α, β ∈ R. Let α1 be the value of α which satisfies (A + B)2 = `A^2 + [(2, 2),(2, 2)]` and α2 be the value of α which satisfies (A + B)2 = B2 . Then |α1 – α2| is equal to ______.
