हिंदी

Let A = `[[2,4],[3,2]]`, `B=[[1,3],[-2,5]]`And `C =[[-2,5],[3,4]]`.Find Each of the Following: 3a − C - Mathematics

Advertisements
Advertisements

प्रश्न

Let A = `[[2,4],[3,2]]`, `B=[[1,3],[-2,5]]`and `c =[[-2,5],[3,4]]`.Find each of the following: 3A − C

योग

उत्तर

`3A -C `

⇒3A−C=3 `[[2   4],[3   2]]-[[-2    5],[3      4]]`

⇒3A−C=`[[6   12],[9     6]]-[[-2    5],[3       4]]`

⇒3A−C=`[[6 +2      12-5],[9-3          6-4]]`

⇒3A−C=`[[8     7],[6     2]]`

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 2.3 | पृष्ठ १८

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

if  `A=[[2,0,0],[0,2,0],[0,0,2]]` then A6=  ......................


If `A=([2,0,1],[2,1,3],[1,-1,0])` find A2 - 5A + 4I and hence find a matrix X such that  A2 - 5A + 4I + X = 0


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: 3A − 2B + 3C


If A =`[[2,3],[5,7]],B =` `[[-1,0 ,2],[3,4,1]]`,`C= [[-1,2,3],[2,1,0]]`find : A + B and B + C


If A = diag (2 − 59), B = diag (11 − 4) and C = diag (−6 3 4), find

B + C − 2A


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 =`[[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 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.

 

Find xyz and t, if

`3[[x     y],[z      t]]=[[x        6],[-1          2t]]+[[4             x+y],[z+t         3]]`

 


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]]`


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

 

 


If  \[A = \begin{bmatrix}2 & 3 \\ 5 & 7\end{bmatrix}\] , find A + AT.
 

 


If A = [aij] is a skew-symmetric matrix, then write the value of  \[\sum_i \sum_j\]  aij.


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


If  \[\begin{bmatrix}xy & 4 \\ z + 6 & x + y\end{bmatrix} = \begin{bmatrix}8 & w \\ 0 & 6\end{bmatrix}\] , write the value of (x + y + z).


If  \[\binom{x + y}{x - y} = \begin{bmatrix}2 & 1 \\ 4 & 3\end{bmatrix}\binom{1}{ - 2}\] , then write the value of (xy).

 

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 ______.


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


Matrices of any order can be added.


`"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 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×