Advertisements
Advertisements
प्रश्न
Find the value of x, if \[\begin{bmatrix}3x + y & - y \\ 2y - x & 3\end{bmatrix} = \begin{bmatrix}1 & 2 \\ - 5 & 3\end{bmatrix}\]
Advertisements
उत्तर
The corresponding elements of two equal matrices are equal.
\[Given: \hspace{0.167em} \begin{bmatrix}3x + y & - y \\ 2y - x & 3\end{bmatrix} = \begin{bmatrix}1 & 2 \\ - 5 & 3\end{bmatrix}\]
\[3x + y = 1 . . . \left( 1 \right) \]
\[ - y = 2\]
\[ \Rightarrow y = - 2\]
Putting the value of y in eq .( 1 )
\[3x + \left( - 2 \right) = 1\]
\[ \Rightarrow 3x - 2 = 1\]
\[ \Rightarrow 3x = 1 + 2\]
\[ \Rightarrow 3x = 3\]
\[ \Rightarrow x = \frac{3}{3} = 1\]
\[ \therefore x = 1\]
APPEARS IN
संबंधित प्रश्न
if `2[[3,4],[5,x]]+[[1,y],[0,1]]=[[7,0],[10,5]]` , find (x−y).
If `[[x-y,z],[2x-y,w]]=[[-1,4],[0,5]]` find the value of x+y.
Find x, y, a and b if
`[[2x-3y,a-b,3],[1,x+4y,3a+4b]]`=`[[1,-2,3],[1,6,29]]`
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]]`
`If [[2x +1 5x],[0 y^2 +1]]``= [[x+3 10],[0 26 ]]`, find the value of (x + y).
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]]`
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 y, if \[\begin{bmatrix}x - y & 2 \\ x & 5\end{bmatrix} = \begin{bmatrix}2 & 2 \\ 3 & 5\end{bmatrix}\]
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.
Which of the given values of x and y make the following pairs of matrices equal? \[\begin{bmatrix}3x + 7 & 5 \\ y + 1 & 2 - 3x\end{bmatrix}, \begin{bmatrix}0 & y - 2 \\ 8 & 4\end{bmatrix}\]
If matrix \[A = \left[ a_{ij} \right]_{2 \times 2}\] where
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 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?
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)]`
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
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 \[A=B\]?
What does the same order of two matrices mean?
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 \[c\] and \[d\] if \[5c-d=11\] and \[4c+3d=24\].
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?
