Question
Given $A=\left[\begin{array}{cc}-3 & 6 \\ 0 & -9\end{array}\right]$ and $A^t$ is its transpose matrix Find $A^t-\frac{1}{3} A$
✓
Answer
$A^t-\frac{1}{3} A $
$ =\left[\begin{array}{cc}-3 & 0 \\ 6 & -9\end{array}\right]-\frac{1}{3}\left[\begin{array}{cc}-3 & 6 \\ 0 & -9\end{array}\right] $
$=\left[\begin{array}{cc}-3 & 0 \\ 6 & -9\end{array}\right]-\left[\begin{array}{cc}-1 & 2 \\ 0 & -3\end{array}\right] $
$ =\left[\begin{array}{cc}-2 & -2 \\ 6 & -6\end{array}\right]$
$ =\left[\begin{array}{cc}-3 & 0 \\ 6 & -9\end{array}\right]-\frac{1}{3}\left[\begin{array}{cc}-3 & 6 \\ 0 & -9\end{array}\right] $
$=\left[\begin{array}{cc}-3 & 0 \\ 6 & -9\end{array}\right]-\left[\begin{array}{cc}-1 & 2 \\ 0 & -3\end{array}\right] $
$ =\left[\begin{array}{cc}-2 & -2 \\ 6 & -6\end{array}\right]$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A bag contains 3 red balls, 4 blue balls and 1 yellow ball, all the balls being identical in shape and size. If a ball is taken out of the bag without looking into it; find the probability that the ball is: red
If a, b, and c are in continued proportion, prove that $\frac{a^2+a b+b^2}{b^2+b c+c^2}=\frac{a}{c}$
→A and B are friends. Ignoring the leap year, find the probability that both friends will have: different birthdays?
Describe the locus for questions 1 to 13 given below:
The locus of a stone dropped from the top of a tower.
f the probability of winning a game is 5/11,what is the probability of losing?
Use the Remainder Theorem to find which of the following is a factor of $2x^3 + 3x^2 – 5x – 6.x + 2$
→If $2x + 1$ is a factor of $2x^2 + ax – 3$, find the value of a.
→Draw the line of symmetry of the following figure and also mark their points of symmetry, if any:
Solve the following inequalities and represent the solution set on a number line:
$-3<-\frac{1}{2}-\frac{2 x}{3}<\frac{5}{6}, x \in R$.
→$-3<-\frac{1}{2}-\frac{2 x}{3}<\frac{5}{6}, x \in R$.
Use the Remainder Theorem to find which of the following is a factor of $2x^3 + 3x^2 – 5x – 6.2x – 1$
→