Advertisements
Advertisements
Question
If \[A = \begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}\] , find A + AT.
Advertisements
Solution
\[Given: A = \begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix} \]
\[ A^T = \begin{bmatrix}1 & 3 \\ 2 & 4\end{bmatrix}\]
\[A + A^T = \begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix} + \begin{bmatrix}1 & 3 \\ 2 & 4\end{bmatrix}\]
\[ \Rightarrow A + A^T = \begin{bmatrix}1 + 1 & 2 + 3 \\ 3 + 2 & 4 + 4\end{bmatrix}\]
\[ \Rightarrow A + A^T = \begin{bmatrix}2 & 5 \\ 5 & 8\end{bmatrix}\]
APPEARS IN
RELATED QUESTIONS
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 [[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,
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]]`
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.
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 \[\begin{bmatrix}2x + y & 3y \\ 0 & 4\end{bmatrix} = \begin{bmatrix}6 & 0 \\ 6 & 4\end{bmatrix}\] , then find x.
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?
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:
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 \[c\] 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 \[\begin{bmatrix}1&3\\2&4\end{bmatrix}\]?
