Advertisements
Advertisements
प्रश्न
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]]`
उत्तर
Since all the corresponding elements of a matrix are equal
\[A = \begin{bmatrix}x - 2 & 3 & 2z \\ 18z & y + 2 & 6z\end{bmatrix} , B = \begin{bmatrix}y & z & 6 \\ 6y & x & 2y\end{bmatrix}\]
\[Here, \]
\[x - 2 = y . . . \left( 1 \right) \]
\[z = 3 . . . \left( 2 \right) \]
\[18z = 6y . . . \left( 3 \right)\]
Putting the value of z in eq . (3) , we get
\[18\left( 3 \right) = 6y\]
\[ \Rightarrow 54 = 6y\]
\[ \Rightarrow y = \frac{54}{6} = 9\]
Putting the value of y in eq . (1) , we get
\[x - 2 = 9\]
\[ \Rightarrow x = 9 + 2\]
\[ \Rightarrow x = 11\]
`∴x=11 , y=9 ` and `z=3`
APPEARS IN
संबंधित प्रश्न
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 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 [[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).
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 − 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 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 \[A = \begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}\] , find A + AT.
If \[\begin{bmatrix}a + b & 2 \\ 5 & b\end{bmatrix} = \begin{bmatrix}6 & 5 \\ 2 & 2\end{bmatrix}\] , then find a.
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 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 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
