Question
Given $A=\left[\begin{array}{ll}1 & 1 \\ 8 & 3\end{array}\right]$ evaluate $A^2- 4A.$
✓
Answer
$\begin{array}{l}A=\left[\begin{array}{ll}1 & 1 \\ 8 & 3\end{array}\right] \end{array} $
$ A^2=A \times A=\left[\begin{array}{ll}1 & 1 \\ 8 & 3\end{array}\right]\left[\begin{array}{ll}1 & 1 \\ 8 & 3\end{array}\right] $
$ =\left[\begin{array}{cc}1+8 & 1+3 \\ 8+24 & 8+9\end{array}\right]$
$=\left[\begin{array}{cc}9 & 4 \\ 32 & 17\end{array}\right] $
$ 4 A=4\left[\begin{array}{ll}1 & 1 \\ 8 & 3\end{array}\right] =\left[\begin{array}{cc}4 & 4 \\ 32 & 12\end{array}\right]$
$\begin{array}{l}A^2-4 A=\left[\begin{array}{cc}9 & 4 \\ 32 & 17\end{array}\right]-\left[\begin{array}{cc}4 & 4 \\ 32 & 12\end{array}\right] \\ \end{array}$
$=\left[\begin{array}{cc}9-4 & 4-4 \\ 32-32 & 17-12\end{array}\right] $
$ A^2-4 A=\left[\begin{array}{ll}5 & 0 \\ 0 & 5\end{array}\right] .$
$ A^2=A \times A=\left[\begin{array}{ll}1 & 1 \\ 8 & 3\end{array}\right]\left[\begin{array}{ll}1 & 1 \\ 8 & 3\end{array}\right] $
$ =\left[\begin{array}{cc}1+8 & 1+3 \\ 8+24 & 8+9\end{array}\right]$
$=\left[\begin{array}{cc}9 & 4 \\ 32 & 17\end{array}\right] $
$ 4 A=4\left[\begin{array}{ll}1 & 1 \\ 8 & 3\end{array}\right] =\left[\begin{array}{cc}4 & 4 \\ 32 & 12\end{array}\right]$
$\begin{array}{l}A^2-4 A=\left[\begin{array}{cc}9 & 4 \\ 32 & 17\end{array}\right]-\left[\begin{array}{cc}4 & 4 \\ 32 & 12\end{array}\right] \\ \end{array}$
$=\left[\begin{array}{cc}9-4 & 4-4 \\ 32-32 & 17-12\end{array}\right] $
$ A^2-4 A=\left[\begin{array}{ll}5 & 0 \\ 0 & 5\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
In the given figure, AC is a diameter of circle, centre O. Chord BD is perpendicular to AC. Write down the angles p, q and r in terms of x .
There are 5 green, 6 black and 7 white balls in a bag. A ball is drawn at random from the bag. Find the probability that it is not white.
Use factor theorem to factorise the following polynominals completely. $x^3 – 13x – 12.$
→A rectangular garden $10$ m by $16$ m is to be surrounded by a concrete walk of uniform width. Given that the area of the walk is $120$ square metres, assuming the width of the walk to be x, form an equation in x and solve it to find the value of x.
→Find whether the value $x=\frac{1}{a^2}$ and $x=\frac{1}{b^2}$ are the solution of the equation:
$a^2 b^2 x^2-\left(a^2+b^2\right) x+1=0, a \neq 0, b \neq 0$
→$a^2 b^2 x^2-\left(a^2+b^2\right) x+1=0, a \neq 0, b \neq 0$
In the figure, given alongside, AB ∥ CD and O is the centre of the circle. If ∠ADC = 25°; find
the angle AEB give reasons in support of your answer.
the angle AEB give reasons in support of your answer.
A man tosses two different coins (one of Rs 2 and another of Rs 5) simultaneously. What is the probability that he gets: at least one head?
Offices in Delhi are open for five days in a week (Monday to Friday). Two employees of an office remain absent for one day in the same particular week. Find the probability that they remain absent on: consecutive day
Write down the equation of the line whose slope is $\frac{3}{2}$ and which passes through the point P , where P divides the line segment joining $A (-2,6)$ and $B (3,-4)$ in the ratio $2: 3$.
→If $\frac{2}{3}$ is a solution of the equation $7 x^2+k x-3=0$, find the value of $k$.
→