Advertisements
Advertisements
Question
If A = diag (2 − 59), B = diag (11 − 4) and C = diag (−6 3 4), find
B + C − 2A
Solution
LaTeX
A = \begin{bmatrix}2 & 0 & 0 \\ 0 & - 5 & 0 \\ 0 & 0 & 9\end{bmatrix} , B = \begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & - 4\end{bmatrix}
\[ \Rightarrow B + C - 2A = \begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & - 4\end{bmatrix} + \begin{bmatrix}- 6 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4\end{bmatrix} - \begin{bmatrix}4 & 0 & 0 \\ 0 & - 10 & 0 \\ 0 & 0 & 18\end{bmatrix}\]
\[ \Rightarrow B + C - 2A = \begin{bmatrix}1 - 6 - 4 & 0 + 0 - 0 & 0 + 0 - 0 \\ 0 + 0 - 0 & 1 + 3 + 10 & 0 + 0 - 0 \\ 0 + 0 - 0 & 0 + 0 - 0 & - 4 + 4 - 18\end{bmatrix}\]
\[ \Rightarrow B + C - 2A = \begin{bmatrix}- 9 & 0 & 0 \\ 0 & 14 & 0 \\ 0 & 0 & - 18\end{bmatrix} = diag\left( - 9 14 - 18 \right)\]
APPEARS IN
RELATED QUESTIONS
if `A=[[2,0,0],[0,2,0],[0,0,2]]` then A6= ......................
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:
`[(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:
`[(cos^2x, sin^2 x),(sin^2 x ,cos^2 x)]+[(sin^2 x, cos^2 x), (cos^2 x, sin^2 x)]`
If F(x) = `[(cosx, -sinx,0), (sinx, cosx, 0),(0,0,1)]` show that F(x)F(y) = F(x + y)
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 − 2B + 3C
If A = diag (2 − 59), B = diag (11 − 4) and C = diag (−6 3 4), find
2A + 3B − 5C
Find matrices X and Y, if X + Y =`[[5 2],[0 9]]`
and X − Y = `[[3 6],[0 -1]]`
Find X if Y =`[[3 2],[1 4]]`and 2X + Y =`[[1 0],[-3 2]]`
Find matrices X and Y, if 2X − Y = `[[6 -6 0],[-4 2 1]]`and X + 2Y =`[[3 2 5],[-2 1 -7 ]]`
f X − Y =`[[1 1 1],[1 1 0],[1 0 0]]` and X + Y = `[[3 5 1],[-1 1 1],[11 8 0]]`find X and Y.
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 z-3 ] + [ y 4 5]=[4 9 12]`
Find x, y satisfying the matrix equations
`x[[2],[1]]+y[[3],[5]]+[[-8],[-11]]=0`
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]]`
Express the matrix \[A = \begin{bmatrix}3 & - 4 \\ 1 & - 1\end{bmatrix}\] as the sum of a symmetric and a skew-symmetric matrix.
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 \[\begin{bmatrix}xy & 4 \\ z + 6 & x + y\end{bmatrix} = \begin{bmatrix}8 & w \\ 0 & 6\end{bmatrix}\] , write the value of (x + y + z).
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).
If A = `[(1, 0, -1),(2, 1, 3 ),(0, 1, 1)]`, then verify that A2 + A = A(A + I), where I is 3 × 3 unit matrix.
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
If A `= [(0,2),(2,0)],` then A2 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 ______.
