मराठी

Evaluate the Following: `[[],[1 2 3],[]]` `[[1 0 2],[2 0 1],[0 1 2]]` `[[2],[4],[6]]` - Mathematics

Advertisements
Advertisements

प्रश्न

Evaluate the following:

`[[],[1  2  3],[]]` `[[1     0      2],[2       0         1],[0          1       2]]` `[[2],[4],[6]]`

बेरीज

उत्तर

`[[],[1  2  3],[]]` `[[1     0      2],[2       0         1],[0          1       2]]` `[[2],[4],[6]]`

`⇒[1+4+0       0+0+3     2+2+6]`  `[[2],[4],[6]]`

`⇒ [5       3        10]` `[[2],[4],[6]]`

`⇒ [10 +12 +60]`

`⇒[82]`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Algebra of Matrices - Exercise 5.3 [पृष्ठ ४१]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
पाठ 5 Algebra of Matrices
Exercise 5.3 | Q 5.2 | पृष्ठ ४१

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Which of the given values of x and y make the following pair of matrices equal?

`[(3x+7, 5),(y+1, 2-3x)] = [(0,y-2),(8,4)]`


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

Find AB


Show that AB ≠ BA in each of the following cases:

`A=[[1       3         0],[1        1          0],[4         1         0]]`And    B=`[[0      1          0],[1        0        0],[0           5          1]]`


If A =  `[[4       2],[-1        1]]` 

, prove that (A − 2I) (A − 3I) = O

 

If A =  `[[1    1],[0    1]]`  show that A2 = `[[1       2],[0          1]]` and A3 = `[[1        3],[0       1]]`


If A = `[[ cos 2θ     sin 2θ],[ -sin 2θ    cos 2θ]]`, find A2.


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

, show that AB = A and BA = B.

 

If A= `[[1        0           -2],[3        -1           0],[-2              1               1]]` B=,`[[0         5           -4],[-2          1             3],[-1          0              2]] and  C=[[1               5              2],[-1           1              0],[0          -1             1]]` verify that A (B − C) = AB − AC.


If


If [1 1 x] `[[1         0            2],[0           2         1],[2            1           0]] [[1],[1],[1]]` = 0, find x.


Find the value of x for which the matrix product`[[2       0           7],[0          1            0],[1       -2       1]]` `[[-x         14x          7x],[0         1            0],[x           -4x             -2x]]`equal an identity matrix.


Solve the matrix equations:

`[x1][[1,0],[-2,-3]][[x],[5]]=0`


Solve the matrix equations:

[2x 3] `[[1       2],[-3      0]] , [[x],[8]]=0`


If `A= [[1,2,0],[3,-4,5],[0,-1,3]]` compute A2 − 4A + 3I3.


`A=[[1,2,2],[2,1,2],[2,2,1]]`, then prove that A2 − 4A − 5I = 0


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


If `P=[[x,0,0],[0,y,0],[0,0,z]]` and `Q=[[a,0,0],[0,b,0],[0,0,c]]` prove that `PQ=[[xa,0,0],[0,yb,0],[0,0,zc]]=QP`


\[A = \begin{bmatrix}\cos \alpha + \sin \alpha & \sqrt{2}\sin \alpha \\ - \sqrt{2}\sin \alpha & \cos \alpha - \sin \alpha\end{bmatrix}\] ,prove that

\[A^n = \begin{bmatrix}\text{cos n α} + \text{sin n α}  & \sqrt{2}\text{sin n  α} \\ - \sqrt{2}\text{sin n α} & \text{cos n α} - \text{sin  n  α} \end{bmatrix}\] for all n ∈ N.

 


Give examples of matrices
A and B such that AB ≠ BA


Give examples of matrices

A and B such that AB = O but BA ≠ O.


Give examples of matrices

 AB and C such that AB = AC but B ≠ CA ≠ 0.

 

If A and B are square matrices of the same order, explain, why in general

(A + B)2 ≠ A2 + 2AB + B2


Let  `A =[[2,-3],[-7,5]]` And `B=[[1,0],[2,-4]]` verify that 

 (A + B)T = AT BT


 For two matrices A and B,   \[A = \begin{bmatrix}2 & 1 & 3 \\ 4 & 1 & 0\end{bmatrix}, B = \begin{bmatrix}1 & - 1 \\ 0 & 2 \\ 5 & 0\end{bmatrix}\](AB)T = BT AT.

 


For the matrices A and B, verify that (AB)T = BT AT, where
\[A = \begin{bmatrix}1 & 3 \\ 2 & 4\end{bmatrix}, B = \begin{bmatrix}1 & 4 \\ 2 & 5\end{bmatrix}\]

If \[\begin{bmatrix}1 & 0 \\ y & 5\end{bmatrix} + 2\begin{bmatrix}x & 0 \\ 1 & - 2\end{bmatrix}\]  = I, where I is 2 × 2 unit matrix. Find x and y.

 


If  \[A = \begin{bmatrix}- 1 & 0 & 0 \\ 0 & - 1 & 0 \\ 0 & 0 & - 1\end{bmatrix}\] , find A3.

 

 


For any square matrix write whether AAT is symmetric or skew-symmetric.


If `[2     1       3]([-1,0,-1],[-1,1,0],[0,1,1])([1],[0],[-1])=A` , then write the order of matrix A.


If A and B are two matrices such n  that AB = B and BA = A , `A^2 + B^2` is equal to


If  \[A = \begin{bmatrix}1 & 2 & x \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix} and B = \begin{bmatrix}1 & - 2 & y \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}\] and AB = I3, then x + y equals 


If \[A = \begin{bmatrix}1 & - 1 \\ 2 & - 1\end{bmatrix}, B = \begin{bmatrix}a & 1 \\ b & - 1\end{bmatrix}\]and (A + B)2 = A2 + B2,   values of a and b are


If  \[A = \begin{bmatrix}\alpha & \beta \\ \gamma & - \alpha\end{bmatrix}\]  is such that A2 = I, then 

 


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


Give an example of matrices A, B and C such that AB = AC, where A is nonzero matrix, but B ≠ C.


If AB = BA for any two square matrices, prove by mathematical induction that (AB)n = AnBn 


A matrix which is not a square matrix is called a ______ matrix.


If A and B are square matrices of the same order, then (kA)′ = ______. (k is any scalar)


Three schools DPS, CVC, and KVS decided to organize a fair for collecting money for helping the flood victims. They sold handmade fans, mats, and plates from recycled material at a cost of Rs. 25, Rs.100, and Rs. 50 each respectively. The numbers of articles sold are given as

School/Article DPS CVC KVS
Handmade/fans 40 25 35
Mats 50 40 50
Plates 20 30 40

Based on the information given above, answer the following questions:

  • What is the total amount of money (in Rs.) collected by schools CVC and KVS?

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×