Advertisements
Advertisements
Question
Which of the given values of x and y make the following pairs of matrices equal? \[\begin{bmatrix}3x + 7 & 5 \\ y + 1 & 2 - 3x\end{bmatrix}, \begin{bmatrix}0 & y - 2 \\ 8 & 4\end{bmatrix}\]
Options
x =\[- \frac{1}{3}\],y = 7
y = 7, x = \[- \frac{2}{3}\]
x = \[- \frac{1}{3}\] 4 =\[- \frac{2}{5}\]
Not possible to find
Solution
Not possible to find
\[Here, \]
\[\begin{bmatrix}3x + 7 & 5 \\ y + 1 & 2 - 3x\end{bmatrix} = \begin{bmatrix}0 & y - 2 \\ 8 & 4\end{bmatrix}\]
`"We know that for two equal matrices the corresponding elements are equal ."`
\[ \therefore 3x + 7 = 0, 5 = y - 2, y + 1 = \text{8 and 2 - 3x }= 4\]
\[ \Rightarrow 3x = - 7, 5 + 2 = y, y = \text{ 8 -1 and - 3x} = 4 - 2\]
\[ \Rightarrow x = \frac{- 7}{3}, y = 7, y = \text{7 and x} = - \frac{2}{3} \]
APPEARS IN
RELATED QUESTIONS
Find x, y, a and b if
`[[2x-3y,a-b,3],[1,x+4y,3a+4b]]`=`[[1,-2,3],[1,6,29]]`
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-y,z],[2x-y,w]]=[[-1,4],[0,5]]`Find X,Y,Z,W.
`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 [[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]]`
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 − 5b should 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 \[\begin{bmatrix}3x + y & - y \\ 2y - x & 3\end{bmatrix} = \begin{bmatrix}1 & 2 \\ - 5 & 3\end{bmatrix}\]
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 \[\begin{bmatrix}a + b & 2 \\ 5 & b\end{bmatrix} = \begin{bmatrix}6 & 5 \\ 2 & 2\end{bmatrix}\] , then find a.
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:
- Which of the following matrix equations represent the information given above?
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?
If A = `[(cos a, - sin a),(sin a, cos a)]`, then A+ A1 = l, if the value of a is:
