मराठी

Solve the following matrix equation for x: [x 1] [[1,0],[−2,0]]=0 - Mathematics

Advertisements
Advertisements

प्रश्न

Solve the following matrix equation for x: `[x 1] [[1,0],[−2,0]]=0`

उत्तर

The given matrix equation is

`[x 1] [[1,0],[−2,0]]=0`

`[x ×1+1×(−2)    x ×0 + 1×0] = 0⇒[x−2   0] = [0  0]`



By the definition of equality of matrices, we get:

x2 = 0x = 2

Thus, the value of x is 2.

 

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
2013-2014 (March) Delhi Set 1

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

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

Find  A + B


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 − C


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

B + C − 2A


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.


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

, find matrix X such that 2A + 3X = 5B.

 

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 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.

 

Find xyz and t, if

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


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

 

 


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


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 ) 


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),(-2, 1)]`, B = `[(2, 3),(3, -4)]` and C = `[(1, 0),(-1, 0)]`, verify: A(B + C) = AB + AC


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


`"A" = [(1,-1),(2,-1)], "B" = [("x", 1),("y", -1)]` and (A + B)2 = A2 + B2, then x + y = ____________.


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 A `= [(0,2),(2,0)],` then A2 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×