मराठी

`If [[X-y Z],[2x-y W]]=[[-1 4],[0 5]]`Find X,Y,Z,W. - Mathematics

Advertisements
Advertisements

प्रश्न

`If [[x-y,z],[2x-y,w]]=[[-1,4],[0,5]]`Find X,Y,Z,W.

Advertisements

उत्तर

Given: `[[x-y       z],[2x-y     w]]=[[-1   4],[0        5]]`

Since all the corresponding elements of a matrix are equal,

x−y=−1

⇒x=−1+y               ...(1)

2x−y=0                    ... (2)

z=4

w=5

Putting the value of x in eq. (2), we get

2(−1+y)−y=0

⇒−2+2y−y=0

⇒−2+y=0

⇒y=2

Putting the value of y in eq. (1), we get

x=−1+2

⇒x=1

 

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Algebra of Matrices - Exercise 5.1 [पृष्ठ ७]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
पाठ 5 Algebra of Matrices
Exercise 5.1 | Q 13 | पृष्ठ ७

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

if `2[[3,4],[5,x]]+[[1,y],[0,1]]=[[7,0],[10,5]]` , find (xy).


If `[[x-y,z],[2x-y,w]]=[[-1,4],[0,5]]` find the value of x+y.


If A= `[(cos alpha, -sin alpha), (sin alpha, cos alpha)]` then A + A' = I then the value of α is  ______.


Find xya and b if

`[[2x-3y,a-b,3],[1,x+4y,3a+4b]]`=`[[1,-2,3],[1,6,29]]`


Find the values of abc and d from the following equations:`[[2a + b,a-2b],[5c-d,4c + 3d ]]`= `[[4,- 3],[11,24]]`

 


`If [[x,3x- y],[2x+z,3y -w ]]=[[3,2],[4,7]]` find x,y,z,w


`If [[2x +1    5x],[0     y^2 +1]]``= [[x+3   10],[0      26 ]]`, find the value of (x + y).


`If [[xy          4],[z+6     x+y ]]``=[[8     w],[0     6]]`, then find the values of X,Y,Z and W . 


Given an example of

a row matrix which is also a column matrix,


For what values of x and y are the following matrices equal?

`A=[[2x+1   2y],[0              y^2 - 5y]]``B=[[x + 3      y^2 +2],[0        -6]]`


Find the values of x and y if

`[[X + 10,Y^2 + 2Y],[0, -4]]`=`[[3x +4,3],[0,y^2-5y]]`


For what values of a and b if A = B, where

`A = [[a + 4        3b],[8        -6]]   B = [[2a +2              b^2+2],[8                    b^2  - 5b]]`

Disclaimer: There is a misprint in the question, b2 − 5should be written instead of b2 − 56.


If  \[\begin{bmatrix}x + 3 & 4 \\ y - 4 & x + y\end{bmatrix} = \begin{bmatrix}5 & 4 \\ 3 & 9\end{bmatrix}\] , find x and y


Find the value of x, if  \[\begin{bmatrix}3x + y & - y \\ 2y - x & 3\end{bmatrix} = \begin{bmatrix}1 & 2 \\ - 5 & 3\end{bmatrix}\]


If matrix A = [1 2 3], write AAT.


If \[A = \begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}\] , find A + AT.


If matrix  \[A = \left[ a_{ij} \right]_{2 \times 2}\] where 

\[a_{ij} = \begin{cases}1 & , if i \neq j \\ 0 & , if i = j\end{cases}\] 

 


If \[A = \frac{1}{\pi}\begin{bmatrix}\sin^{- 1} \left( \ pix \right) & \ tan^{- 1} \left( \frac{x}{\pi} \right) \\ \sin^{- 1} \left( \frac{x}{\pi} \right) & \cot^{- 1} \left( \ pix \right)\end{bmatrix}, B = \frac{1}{\pi}\begin{bmatrix}- \cos^{- 1} \left( \ pix \right) & \tan^{- 1} \left( \frac{x}{\pi} \right) \\ \sin^{- 1} \left( \frac{x}{\pi} \right) & - \tan^{- 1} \left( \ pix \right)\end{bmatrix}\]

A − B is equal to


If A `= [(0,-1,2),(1,0,3),(-2,-3,0)],` then A + 2AT equals


On her birthday, Seema decided to donate some money to the children of an orphanage home. If there were 8 children less, everyone would have got Rs.10 more. However, if there were 16 children more, everyone would have got Rs. 10 less. Let the number of children be x and the amount distributed by Seema for one child be y(in Rs.).

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

  • The equations in terms x and y are ____________.

On her birthday, Seema decided to donate some money to the children of an orphanage home. If there were 8 children less, everyone would have got Rs.10 more. However, if there were 16 children more, everyone would have got Rs. 10 less. Let the number of children be x and the amount distributed by Seema for one child be y(in Rs.)

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

  • The number of children who were given some money by Seema, is ____________.

On her birthday, Seema decided to donate some money to the children of an orphanage home. If there were 8 children less, everyone would have got Rs.10 more. However, if there were 16 children more, everyone would have got Rs. 10 less. Let the number of children be x and the amount distributed by Seema for one child be y(in Rs.)

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

  • How much amount is given to each child by Seema?

On her birthday, Seema decided to donate some money to the children of an orphanage home. If there were 8 children less, everyone would have got Rs.10 more. However, if there were 16 children more, everyone would have got Rs. 10 less. Let the number of children be x and the amount distributed by Seema for one child be y(in Rs.)

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

  • How much amount Seema spends in distributing the money to all the students of the Orphanage?

Two matrices A = [aÿ] and B = [bÿ] are said to be equal if.


If A = `[(cos a, - sin a),(sin a, cos a)]`, then A+ A1 = l, if the value of a is:


Choose the correct answer in the following questions

If A = `[(alpha, beta),(y, - a)]` is such that A2 = I, then


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×