मराठी

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

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 4: Algebra of Matrices - Exercise 5.1 [पृष्ठ ७]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
पाठ 4 Algebra of Matrices
Exercise 5.1 | Q 13 | पृष्ठ ७

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

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


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

 


Find x, y and z so that A = B, where`A= [[x-2,3,2x],[18z,y+2,6x]],``b=[[y,z,6],[6y,x,2y]]`


`If [[x + 3 , z + 4 ,     2y-7 ],[4x + 6,a-1,0 ],[b-3,3b,z + 2c ]]= [[0,6,3y-2],[2x,-3,2c-2],[2b + 4,-21,0]]`Obtain the values of a, b, c, x, y and z.

 


`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,


Find the values of x and y if

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


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 from the following: `[[2x - y          5],[ 3                         y ]]` = `[[6            5 ],[3         - 2\]]`


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


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


If matrix A = [1 2 3], write AAT.


if  \[\begin{bmatrix}2x + y & 3y \\ 0 & 4\end{bmatrix} = \begin{bmatrix}6 & 0 \\ 6 & 4\end{bmatrix}\]  , then find x.


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 = `[[3,1] , [7,5]]`, find the values of x and y such that A2 + xI2 = yA.


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 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?

Choose the correct answer in the following questions

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


Two matrices are equal if and only if which two conditions are satisfied?


What does the same order of two matrices mean?


Determine whether the following matrices are equal: \[A=\begin{bmatrix}2&3\\1&5\end{bmatrix}\quad\text{and}\quad B=\begin{bmatrix}2&3\\1&5\end{bmatrix}.\]


From \[\begin{bmatrix}2a+b&a-2b\\5c-d&4c+3d\end{bmatrix}=\begin{bmatrix}4&-3\\11&24\end{bmatrix},\] which equation is obtained by equating the corresponding elements in position \[(1,2)\]?


Find \[a\] and \[b\] if \[2a+b=4\] and \[a-2b=-3\].


Find the values of \[a,b,c\], and \[d\] in \[\begin{bmatrix}2a+b&a-2b\\5c-d&4c+3d\end{bmatrix}=\begin{bmatrix}4&-3\\11&24\end{bmatrix}.\]


Given \[P=\begin{bmatrix}1&2\\3&4\end{bmatrix}\] and \[Q=\begin{bmatrix}1&2\\3&5\end{bmatrix}\], why is \[P\ne Q\]?


Which statement correctly compares \[\begin{bmatrix}1&2\\3&4\end{bmatrix}\] and \[\begin{bmatrix}1&3\\2&4\end{bmatrix}\]?


What follows if even one corresponding entry differs between two matrices having the same order?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×