हिंदी

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

Advertisements
Advertisements

प्रश्न

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

रिक्त स्थान भरें

उत्तर

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

Explanation:

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

For example a rectangular matrix is A = [aij]m × n, where m ≠ n.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Matrices - Exercise [पृष्ठ ६२]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
अध्याय 3 Matrices
Exercise | Q 72 | पृष्ठ ६२

वीडियो 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)]`


Compute the indicated product:

`[(a,b),(-b,a)][(a,-b),(b,a)]`


Compute the indicated products

`[(2,3,4),(3,4,5),(4,5,6)][(1,-3,5),(0,2,4), (3,0,5)]`


If A = `[[1     0],[0        1]]`,B`[[1            0],[0       -1]]`

and C= `[[0      1],[1       0]]` 

, then show that A2 = B2 = C2 = I2.

 

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.


\[A = \begin{bmatrix}3 & 1 \\ - 1 & 2\end{bmatrix} and \text{ I} = \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}\]


If


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:

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


If f (x) = x2 − 2x, find f (A), where A=


Find a 2 × 2 matrix A such that `A=[[1,-2],[1,4]]=6l_2`


If `A=[[1,1],[0,1]] ,` Prove that `A=[[1,n],[0,1]]` for all positive integers n.


If BC are n rowed square matrices and if A = B + CBC = CBC2 = O, then show that for every n ∈ NAn+1 = Bn (B + (n + 1) C).

 

Let A and B be square matrices of the same order. Does (A + B)2 = A2 + 2AB + B2 hold? If not, why?

 

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

(A + B)2 ≠ A2 + 2AB + B2


If A and B are square matrices of the same order such that AB = BA, then show that (A + B)2 = A2 + 2AB + B2.

 

Let `A=[[1,1,1],[3,3,3]],B=[[3,1],[5,2],[-2,4]]` and `C=[[4,2],[-3,5],[5,0]]`Verify that AB = AC though B ≠ CA ≠ O.

 

 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.

 


If the matrix \[A = \begin{bmatrix}5 & 2 & x \\ y & z & - 3 \\ 4 & t & - 7\end{bmatrix}\]  is a symmetric matrix, find xyz and t.
 

 


 If \[A = \begin{bmatrix}4 & 3 \\ 1 & 2\end{bmatrix} and B = \binom{ - 4}{ 3}\] 

write AB.

 

If  \[A = \begin{bmatrix}1 \\ 2 \\ 3\end{bmatrix}\] write AAT.

 


If \[A = \begin{bmatrix}1 & 1 \\ 1 & 1\end{bmatrix}\] satisfies A4 = λA, then write the value of λ.

 

 


For a 2 × 2 matrix A = [aij] whose elements are given by 

\[a_{ij} = \frac{i}{j}\] , write the value of a12.
 

If  \[A = \begin{bmatrix}1 & a \\ 0 & 1\end{bmatrix}\]then An (where n ∈ N) equals 

 


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

 


If A = `[(0, 1),(1, 0)]`, then A2 is equal to ______.


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?

If A = `[(a, b),(b, a)]` and A2 = `[(α, β),(β, α)]`, then ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×