हिंदी

If A' = [(–2, 3),(1, 2)] and B = [(–1, 0),(1, 2)], then find (A + 2B)'

Advertisements
Advertisements

प्रश्न

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

योग
Advertisements

उत्तर

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

So, A = `[(-2, 1),(3, 2)]`   ...[∵ (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 ६७]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 3 Matrices
EXERCISE 3.3 | Q 4. | पृष्ठ ६७

संबंधित प्रश्न

Matrix A = `[(0,2b,-2),(3,1,3),(3a,3,-1)]`is given to be symmetric, find values of a and b


If A is a skew symmetric matric of order 3, then prove that det A  = 0


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 = `[(sin α, cos α), (-cos α, sin α)]`, then verify that A'A = I


Show that the matrix A = `[(1, -1, 5),(-1, 2, 1),(5, 1, 3)]` is a symmetric matrix.


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


Find `1/2` (A + A') and `1/2` (A – A'), when A = `[(0, a, b),(-a, 0, c),(-b, -c, 0)]`


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

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


Show that the matrix B'AB is symmetric or skew symmetric according as A is symmetric or skew symmetric.


If A is a square matrix, then AA is a


If A and B are symmetric matrices, then ABA is


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


The matrix  \[A = \begin{bmatrix}0 & - 5 & 8 \\ 5 & 0 & 12 \\ - 8 & - 12 & 0\end{bmatrix}\] is a 

 

The matrix   \[A = \begin{bmatrix}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{bmatrix}\] is

 


Show that a matrix which is both symmetric and skew symmetric is a zero matrix.


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 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.


______ matrix is both symmetric and skew-symmetric matrix.


If A and B are symmetric matrices, then AB – BA is a ______.


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


AA′ is always a symmetric matrix for any matrix A.


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


If A and B are symmetric matrices of the same order, then ____________.


If A = `[(3, "x" - 1),(2"x" + 3, "x" + 2)]` is a symmetric matrix, then x = ____________.


If A is any square matrix, then which of the following is skew-symmetric?


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 ______.


Number of symmetric matrices of order 3 × 3 with each entry 1 or – 1 is ______.


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 ______.


For what value of k the matrix `[(0, k),(-6, 0)]` is a skew symmetric matrix?


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


Which of the following is correct?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×