हिंदी

Construct a 3 × 4 Matrix A = [Aij] Whose Elements Aij Are Given By: Aij = 2i - Mathematics

Advertisements
Advertisements

प्रश्न

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

 aij = 2i

उत्तर

aij = 2i

Here,

`a_11=2(1)=2 , a_12=2(1)=2,a_13=2(1)=2, a_14=2(1)=2`

`a_21=2(2)=4,a_22=2(2)=4, a_23=2(2)=4 , a_24 = 2(2)=4`

`a_31=2(3)=6, a_23=2(3)=6,a_33=2(3)=6  and a_34=2(3)=6` 

So, the required matrix is `[[2  2  2  2  ],[4  4  4  4],[6  6  6  6 ]]`

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 6.3 | 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.


Write the element a23 of a 3 ✕ 3 matrix A = (aij) whose elements aij are given by `a_(ij)=∣(i−j)/2∣`


If `[[3x,7],[-2,4]]=[[8,7],[6,4]]`, find the value of x


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


Let A be a matrix of order 3 × 4. If R1 denotes the first row of A and C2 denotes its second column, then determine the orders of matrices R1 and C2


If A = [aij] =`[[2,3,-5],[1,4,9],[0,7,-2]]`and B = [bij] `[[2,-1],[-3,4],[1,2]]`

then find (i) a22 + b21 (ii) a11 b11 + a22 b22

 

 


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


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

`a_(ij)=|2_i - 3_i|/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 = 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

`a_(ij)= (i-j)/(i+j )`


Construct a 4 × 3 matrix whose elements are

 aij = 


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=[[cos θ, i sinθ],[i sinθ,cosθ]]` then prove by principle of mathematical induction that `A^n=[[cos  nθ,i sinθ],[i sin nθ,cos nθ]]` for all `n  ∈ N.`


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

 

The cooperative stores of a particular school has 10 dozen physics books, 8 dozen chemistry books and 5 dozen mathematics books. Their selling prices are Rs. 8.30, Rs. 3.45 and Rs. 4.50 each respectively. Find the total amount the store will receive from selling all the items.

 

If A and B are symmetric matrices, then write the condition for which AB is also symmetric.


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


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.


Matrix A = \[\begin{bmatrix}0 & 2b & - 2 \\ 3 & 1 & 3 \\ 3a & 3 & - 1\end{bmatrix}\]  is given to be symmetric, find values of a and b.

 


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 \[A = \begin{bmatrix}\cos \theta & - \sin \theta \\ \sin \theta & \cos \theta\end{bmatrix}\]  then AT + A = I2, if


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×