हिंदी

If A' = and[-2312]andB=[-1012] then find (A + 2B)' - Mathematics

Advertisements
Advertisements

प्रश्न

if A' = `[(-2,3),(1,2)] and B = [(-1,0),(1,2)]`  then find (A + 2B)'

योग

उत्तर

Given, A' = `[(-2,3),(1,2)]` and` "B" = [(-1,0),(1,2)]`

so, A = `[(-2,1),(3,2)]`     [Because(A)' = A]

Now, (A + 2B) = `[(-2,1),(3,2)] + 2 [(-1,0),(1,2)]`

`= [(-2,1),(3,2)] + [(-2,0),(2,4)]`

`= [(-2 - 2, 1 + 0),(3 + 2, 2 + 4)]`

`= [(-4, 1),(5,6)]`

(A + 2B)' = `[(-4 , 5), (1,6)]`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Matrices - Exercise 3.3 [पृष्ठ ८८]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 12
अध्याय 3 Matrices
Exercise 3.3 | Q 4 | पृष्ठ ८८

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

If `A = [(-1,2,3),(5,7,9),(-2,1,1)]  "and"  B = [(-4,1,-5),(1,2,0),(1,3,1)]` then verify that (A+ B)' = A' + B'


if `A = [(-1,2,3),(5,7,9),(-2,1,1)] and B = [(-4,1,-5),(1,2,0),(1,3,1)]` then verify that (A- B)' = A' - B'


if `A' [(3,4),(-1, 2),(0,1)] and B = [((-1,2,1),(1,2,3))]` then verify that (A + B)' = A' + B'


if `A' [(3,4),(-1, 2),(0,1)] and B = [((-1,2,1),(1,2,3))]` then verify that (A - B)' = A' - B'


For the matrices A and B, verify that (AB)′ = B'A'  where `A =[(0), (1),(2)] , B =[1 , 5, 7]`


Show that the matrix  A = `[(0,1,-1),(-1,0,1),(1,-1,0)]` is a skew symmetric matrix.


For the matrix A = `[(1,5),(6,7)]` verify that (A - A') is a skew symmetric matrix.


Express the following matrices as the sum of a symmetric and a skew symmetric matrix:

`[(3,3,-1),(-2,-2,1),(-4,-5,2)]`


If A and B are symmetric matrices, prove that AB − BA is a skew symmetric matrix.


Find the values of x, y, z if the matrix `A = [(0,2y,z),(x,y,-z),(x , -y,z)]` satisfy the equation A'A = I.


If \[A = \begin{bmatrix}1 & 2 \\ 0 & 3\end{bmatrix}\] is written as B + C, where B is a symmetric matrix and C is a skew-symmetric matrix, then B is equal to.


For what value of x, is the matrix  \[A = \begin{bmatrix}0 & 1 & - 2 \\ - 1 & 0 & 3 \\ x & - 3 & 0\end{bmatrix}\]  a skew-symmetric matrix?


If a matrix A is both symmetric and skew-symmetric, then


The matrix \[\begin{bmatrix}0 & 5 & - 7 \\ - 5 & 0 & 11 \\ 7 & - 11 & 0\end{bmatrix}\] is


If A = [aij] is a square matrix of even order such that aij = i2 − j2, then 


If \[A = \begin{bmatrix}2 & 0 & - 3 \\ 4 & 3 & 1 \\ - 5 & 7 & 2\end{bmatrix}\]  is expressed as the sum of a symmetric and skew-symmetric matrix, then the symmetric matrix is  


If the matrix `((6,-"x"^2),(2"x"-15 , 10))` is symmetric, find the value of x.


Express the matrix A as the sum of a symmetric and a skew-symmetric matrix, where A = `[(2, 4, -6),(7, 3, 5),(1, -2, 4)]`


If A and B are symmetric matrices of the same order, then (AB′ –BA′) is a ______.


If A and B are two skew-symmetric matrices of same order, then AB is symmetric matrix if ______.


If A = `[(0, 1),(1, 1)]` and B = `[(0, -1),(1, 0)]`, show that (A + B)(A – B) ≠ A2 – B2 


Show that A′A and AA′ are both symmetric matrices for any matrix A.


If A = `[(cosalpha, sinalpha),(-sinalpha, cosalpha)]`, and A–1 = A′, find value of α


If the matrix `[(0, "a", 3),(2, "b", -1),("c", 1, 0)]`, is a skew symmetric matrix, find the values of a, b and c.


If A, B are square matrices of same order and B is a skew-symmetric matrix, show that A′BA is skew-symmetric.


The matrix `[(1, 0, 0),(0, 2, 0),(0, 0, 4)]` is a ______.


If A is a skew-symmetric matrix, then A2 is a ______.


If A and B are symmetric matrices of same order, then AB is symmetric if and only if ______.


If A and B are any two matrices of the same order, then (AB)′ = A′B′.


If A `= [(6,8,5),(4,2,3),(9,7,1)]` is the sum of a symmetric matrix B and skew-symmetric matrix C, then B is ____________.


The diagonal elements of a skew symmetric matrix are ____________.


If ax4 + bx3 + cx2 + dx + e = `|(2x, x - 1, x + 1),(x + 1, x^2 - x, x - 1),(x - 1, x + 1, 3x)|`, then the value of e is ______.


If `[(2, 0),(5, 4)]` = P + Q, where P is symmetric, and Q is a skew-symmetric matrix, then Q is equal to ______.


The value of |A|, if A = `[(0, 2x - 1, sqrt(x)),(1 - 2x, 0, 2sqrt(x)),(-sqrt(x), -2sqrt(x), 0)]`, where x ∈ R+, is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×