हिंदी

Construct a 2 × 2 Matrix Whose Elements Aij Are Given By: `A_(Ij)=[[2_I - 3_I]]/2` - Mathematics

Advertisements
Advertisements

प्रश्न

Construct a 2 × 2 matrix whose elements aij are given by:

`a_(ij)=|2_i - 3_i|/2`

योग

उत्तर

`a_(ij)=[[2_i - 3_i]]/2`

Here,

`a_11=|2(1)-3(1)|/2=|2-3|/2=[|-1|]/2=1/2 , a_12 = |2(1)-3(2)|/2=[|2-6|]/2=[|-4|]/2=2`

`a_21=|2(2)-3(1)|/2=|4-3|/2=1/2  , a_22= |2(2)-3(2)|/2=|4-6|/2=|-2|/2=1`

so, the required matrix is `[[1/2   2 ], [1/2   1]]`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 5: Algebra of Matrices - Exercise 5.1 [पृष्ठ ७]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
अध्याय 5 Algebra of Matrices
Exercise 5.1 | Q 5.5 | पृष्ठ ७

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

If `A=[[2,0,1],[2,1,3],[1,-1,0]]` , find A2 − 5 A + 16 I.


Write the element a12 of the matrix A = [aij]2 × 2, whose elements aij are given by aij = e2ix sin jx.


If A= `((1,0,2),(0,2,1),(2,0,3))` and A3 - 6A2 +7A + kI3 = O find k.


Find the maximum value of `|(1,1,1),(1,1+sintheta,1),(1,1,1+costheta)|`


If a matrix has 8 elements, what are the possible orders it can have? What if it has 5 elements?


Construct a 2 × 2  matrix whose elements `a_(ij)`

are given by: `(i+j)^2/2`


Construct a 2 × 2 matrix whose elements aij are given by:

`aij=(i-j)^2/2`


Construct a 2 × 2 matrix whose elements aij are given by:

`a_(ij)=(i-2_j)^2/2`


Construct a 2 × 2 matrix whose elements aij are given by:

`a_(ij)= (2i +j)^2/2`


Construct a 2 × 2 matrix whose elements aij are given by:

`a_(ij)=e^(2ix) sin (xj)`


Construct a 3 × 4 matrix A = [aij] whose elements aij are given by:

aij i + j


Construct a 3 × 4 matrix A = [ajj] whose elements ajj are given by:

ajj = i − j


Construct a 3 × 4 matrix A = [aij] whose elements aij are given by:

`a_(ij)=1/2= -3i + j `


Construct a 4 × 3 matrix whose elements are

`a_(ij)=2_i+ i/j`


Construct a 4 × 3 matrix whose elements are

 aij = 


Given an example of

 a triangular matrix


The sales figure of two car dealers during January 2013 showed that dealer A sold 5 deluxe, 3 premium and 4 standard cars, while dealer B sold 7 deluxe, 2 premium and 3 standard cars. Total sales over the 2 month period of January-February revealed that dealer A sold 8 deluxe 7 premium and 6 standard cars. In the same 2 month period, dealer B sold 10 deluxe, 5 premium and 7 standard cars. Write 2 × 3 matrices summarizing sales data for January and 2-month period for each dealer.


If A = diag (abc), show that An = diag (anbncn) for all positive integer n.

 

If A is a square matrix, using mathematical induction prove that (AT)n = (An)T for all n ∈ ℕ.

 

A matrix X has a + b rows and a + 2 columns while the matrix Y has b + 1 rows and a + 3 columns. Both matrices XY and YX exist. Find a and b. Can you say XY and YX are of the same type? Are they equal.

 

If B is a symmetric matrix, write whether the matrix AB AT is symmetric or skew-symmetric.


If A is a skew-symmetric and n ∈ N such that (An)T = λAn, write the value of λ.


If A is a skew-symmetric matrix and n is an odd natural number, write whether An is symmetric or skew-symmetric or neither of the two.


If A is a skew-symmetric matrix and n is an even natural number, write whether An is symmetric or skew symmetric or neither of these two.


If \[\begin{bmatrix}x & 1\end{bmatrix}\begin{bmatrix}1 & 0 \\ - 2 & 0\end{bmatrix} = O\]  , find x.


`If A = ([3   5] , [7     9])` is written as A = P + Q, where as A = p + Q , Where  P is a symmetric matrix and Q is skew symmetric matrix , then wqrite the matrix P. 


Let and be matrices of orders 3 x 2 and 2 x 

4 respectively. Write the order of matrix AB. 


If the matrix AB is zero, then


If \[A = \begin{bmatrix}5 & x \\ y & 0\end{bmatrix}\]  and A = AT, then


If A is 3 × 4 matrix and B is a matrix such that A'B and BA' are both defined. Then, B is of the type 


If `3"A" - "B" = [(5,0),(1,1)] and "B" = [(4,3),(2,5)]`, then find the martix A.


Find a matrix A such that 2A − 3B + 5C = 0, where B =`[(-2, 2, 0), (3, 1, 4)] and  "C" = [(2, 0, -2),(7, 1, 6)]`.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×