हिंदी

Compute the Following Sums: `[[2 1 3],[0 3 5],[-1 2 5]]`+ `[[1 -2 3],[2 6 1],[0 -3 1]]` - Mathematics

Advertisements
Advertisements

प्रश्न

Compute the following sums:

`[[2    1   3],[0   3   5],[-1   2   5]]`+ `[[1 -2     3],[2            6        1],[0   -3       1]]`

उत्तर

`[[2    1   3],[0   3   5],[-1   2   5]]`+ `[[1 -2     3],[2            6        1],[0   -3       1]]`

`⇒ [[2+1      1-2      3+3],[0+2     3+6      5+1],[-1+0      2-3      5+1]]`

`⇒[[3     -1       6],[2                      6],[-1      -1    6]]`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 5: Algebra of Matrices - Exercise 5.2 [पृष्ठ १८]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
अध्याय 5 Algebra of Matrices
Exercise 5.2 | Q 1.2 | पृष्ठ १८

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

If `A=[[1,2,2],[2,1,2],[2,2,1]]` ,then show that `A^2-4A-5I=0` and hence find A-1.


Let `A = [(2,4),(3,2)] , B = [(1,3),(-2,5)], C = [(-2,5),(3,4)]`

Find  A + B


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)]`


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: 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 : 


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 ]]`


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 xy satisfying the matrix equations

`[x     y + 2    z-3 ] +  [  y       4          5]=[4        9        12]`


Find xy 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 the value of λ, a non-zero scalar, if λ


Find a matrix X such that 2A + B + X = O, where

`A= [[-1      2],[3        4]],B= [[3       -2],[1          5]]`


Find a matrix X such that 2A + B + X = O, where 

 If A = `[[8            0],[4    -2],[3         6]]` and B = `[[2       -2],[4           2],[-5          1]]`

, then find the matrix X of order 3 × 2 such that 2A + 3X = 5B.

 

If X and Y are 2 × 2 matrices, then solve the following matrix equations for X and Y.

`2X + 3Y = [[2,3],[4,0]], 3X+2Y = [[-2,2],[1,-5]]`


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]]`


 Let  \[A = \begin{bmatrix}3 & 2 & 7 \\ 1 & 4 & 3 \\ - 2 & 5 & 8\end{bmatrix} .\] Find matrices X and Y such that X + Y = A, where X is a symmetric and Y is a skew-symmetric matrix

 


Express the matrix \[A = \begin{bmatrix}3 & - 4 \\ 1 & - 1\end{bmatrix}\]  as the sum of a symmetric and a skew-symmetric matrix.

 

 


If  \[A = \begin{bmatrix}i & 0 \\ 0 & i\end{bmatrix}\] , write A2.
 

 


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 \[I = \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}, J = \begin{bmatrix}0 & 1 \\ - 1 & 0\end{bmatrix} and B = \begin{bmatrix}\cos \theta & \sin \theta \\ - \sin \theta & \cos \theta\end{bmatrix}\] 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 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


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 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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×