मराठी

If [ a + B 2 5 B ] = [ 6 5 2 2 ] , Then Find A.

Advertisements
Advertisements

प्रश्न

If \[\begin{bmatrix}a + b & 2 \\ 5 & b\end{bmatrix} = \begin{bmatrix}6 & 5 \\ 2 & 2\end{bmatrix}\] , then find a.

बेरीज
Advertisements

उत्तर

The corresponding elements of two equal matrices are equal.

\[\Rightarrow \begin{bmatrix}a + b & 2 \\ 5 & b\end{bmatrix} = \begin{bmatrix}6 & 5 \\ 2 & 2\end{bmatrix}\]

\[ \Rightarrow a + b = 6 . . . \left( 1 \right)\]

\[ \therefore b = 2\]

Putting the value of b in eq . ( 1 )

\[a + 2 = 6\]

\[ \Rightarrow a = 6 - 2\]

\[ \therefore a = 4\]

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 4: Algebra of Matrices - Exercise 5.6 [पृष्ठ ६३]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
पाठ 4 Algebra of Matrices
Exercise 5.6 | Q 40 | पृष्ठ ६३

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.


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]]`

 


Find xy 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 abcxy and z.

 


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


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]]`


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 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.


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?

What is the value of a, b, c and 'd' from the following equation?

`[(2a + b, a - 2b),(5c - d, 4c + 3d)] = [(4, -3),(11, 24)]`


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


If \[A=[a_{ij}]_{m \times n}\] and \[B=[b_{ij}]_{m \times n}\], which statement expresses \[A=B\]?


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 \[(2,1)\]?


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×