हिंदी

Find X If Y =`[[3 2],[1 4]]`And 2x + Y =`[[1 0],[-3 2]]` - Mathematics

Advertisements
Advertisements

प्रश्न

Find X if Y =`[[3       2],[1      4]]`and 2X + Y =`[[1       0],[-3        2]]`

योग

उत्तर

Given : `2X+Y =[[1         0],[-3        2]]`

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

`⇒ 2X =[[1     0],[-3      2]]-[[3      2],[1     4]]`

`⇒2X=[[1-3           0-2],[-3-1           2-4]]`

`⇒ 2X =[[-2      -2],[-4       -2]]`

`⇒ X=1/2 [[-2       -2],[-4       -2]]`

`⇒X=[[-1        -1],[-2           -1]]`

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 8 | पृष्ठ १८

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

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.


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

Find  A + B


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: 

`[(-1,4, -6),(8,5,16),(2,8,5)] + [(12,7,6),(8,0,5),(3,2,4)]`


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


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 matrices X and Y, if X + Y =`[[5     2],[0       9]]`

and X − Y =  `[[3       6],[0   -1]]`

 


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 =`[[9     1],[7      8]],B=[[1      5],[7      12]]`find matrix C such that 5A + 3B + 2C is a null matrix.


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


Find xyz and t, if

`2[[x         5],[z         t]]+[[x           6],[-1          2t]]=[[7            14],[15        14]]`


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]]`


 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


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  \[x\binom{2}{3} + y\binom{ - 1}{1} = \binom{10}{5}\] , find the value of x.


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.

 

 


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),(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)B = aB + bB


If A = `[(0, -x),(x, 0)]`, B = `[(0, 1),(1, 0)]` and x2 = –1, then show that (A + B)2 = A2 + B2


If A = `[(1, 2),(4, 1)]`, find A2 + 2A + 7I.


Matrix multiplication is ______ over addition.


Matrices of any order can be added.


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×