Advertisements
Advertisements
Question
If \[\begin{bmatrix}a + b & 2 \\ 5 & b\end{bmatrix} = \begin{bmatrix}6 & 5 \\ 2 & 2\end{bmatrix}\] , then find a.
Solution
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 )
\[a + 2 = 6\]
\[ \Rightarrow a = 6 - 2\]
\[ \therefore a = 4\]
APPEARS IN
RELATED QUESTIONS
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 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,3x- y],[2x+z,3y -w ]]=[[3,2],[4,7]]` find x,y,z,w
`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 [[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 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 \[A = \frac{1}{\pi}\begin{bmatrix}\sin^{- 1} \left( \ pix \right) & \ tan^{- 1} \left( \frac{x}{\pi} \right) \\ \sin^{- 1} \left( \frac{x}{\pi} \right) & \cot^{- 1} \left( \ pix \right)\end{bmatrix}, B = \frac{1}{\pi}\begin{bmatrix}- \cos^{- 1} \left( \ pix \right) & \tan^{- 1} \left( \frac{x}{\pi} \right) \\ \sin^{- 1} \left( \frac{x}{\pi} \right) & - \tan^{- 1} \left( \ pix \right)\end{bmatrix}\]
A − B is equal to
If A `= [(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?
Two matrices A = [aÿ] and B = [bÿ] are said to be equal if.
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:
