Advertisements
Advertisements
Question
if `2[[3,4],[5,x]]+[[1,y],[0,1]]=[[7,0],[10,5]]` , find (x−y).
Advertisements
Solution
It is given that `2[[3,4],[5,x]]+[[1,y],[0,1]]=[[7,0],[10,5]].`
Let us simplify the left hand side as below:
`[[2xx3,2xx4],[2xx5,2x]]+[[1,y],[0,1]]=[[7,0],[10,5]]`
`[[6,8],[10,2x]]+[[1,y],[0,1]]=[[7,0],[10,5]]`
`[[6+1,8+y],[10,2x+1]]=[[7,0],[10,5]]`
`[[7,8+y],[10,2x+1]]=[[7,0],[10,5]]`
Two matrices are equal if and only if their corresponding entries are equal.
So, equating the corresponding entries, we get:
8+y=0⇒y=−8
and
2x+1=5 ⇒2x=4 ⇒x=2
So, (x − y) = [2 − (−8)] = 2 + 8 = 10
Thus, the value of (x − y) is 10.
APPEARS IN
RELATED QUESTIONS
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-y,z],[2x-y,w]]=[[-1,4],[0,5]]`Find X,Y,Z,W.
`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 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 \[A = \begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}\] , 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 \[A = \frac{1}{\pi}\begin{bmatrix}\sin^{- 1} \left( \ pix \right) & \ tan^{- 1} \left( \frac{x}{\pi} \right) \\ \sin^{- 1} \left( \frac{x}{\pi} \right) & \cot^{- 1} \left( \ pix \right)\end{bmatrix}, B = \frac{1}{\pi}\begin{bmatrix}- \cos^{- 1} \left( \ pix \right) & \tan^{- 1} \left( \frac{x}{\pi} \right) \\ \sin^{- 1} \left( \frac{x}{\pi} \right) & - \tan^{- 1} \left( \ pix \right)\end{bmatrix}\]
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:
- 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:
Two matrices are equal if and only if which two conditions are satisfied?
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 \[c\] and \[d\] if \[5c-d=11\] and \[4c+3d=24\].
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?
