Given A= [ ll p & 0 0 & 2 ], B= [ cc 0 & -q 1 & 0 ], C= [ cc 2 & … - Vidyadip

Question

Given $A=\left[\begin{array}{ll}p & 0 \\ 0 & 2\end{array}\right], B=\left[\begin{array}{cc}0 & -q \\ 1 & 0\end{array}\right], C=\left[\begin{array}{cc}2 & -2 \\ 2 & 2\end{array}\right]$ and if $B A=C^2$, find $p$ and $q$.

✓

Answer

$\begin{aligned} & BA =\left[\begin{array}{cc}0 & - q \\ 1 & 0\end{array}\right]\left[\begin{array}{ll} p & 0 \\ 0 & 2\end{array}\right] \\ & =\left[\begin{array}{cc}0-0 & 0-2 q \\ p -0 & 0+0\end{array}\right] \\ & =\left[\begin{array}{cc}0 & -2 q \\ p & 0\end{array}\right] \\ & C ^2=\left[\begin{array}{cc}2 & -2 \\ 2 & 2\end{array}\right]\left[\begin{array}{cc}2 & -2 \\ 2 & 2\end{array}\right] \\ & =\left[\begin{array}{cc}4-4 & -4-4 \\ 4+4 & -4+4\end{array}\right] \\ & =\left[\begin{array}{cc}0 & -8 \\ 8 & 0\end{array}\right] \\ & \text { But BA }= C ^2 \\ & {\left[\begin{array}{cc}0 & -2 q \\ p & 0\end{array}\right]=\left[\begin{array}{cc}0 & -8 \\ 8 & 0\end{array}\right]} \\ & -2 q =-8\end{aligned}$
$
\begin{aligned}
& q=\frac{8}{2}=4 \\
& p=8
\end{aligned}
$
$\therefore$ The value of $p=8$ and $q=4$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "[5 Mark Questions]" from Algebra→Algebra — all question types→MATHS STD 10 question papers→Tamilnadu Board STD 10 question papers→Tamilnadu Board question paper generator→

Similar questions

If $\cot \theta+\tan \theta= x$ and $\sec \theta-\cos \theta= y$, then prove that $\left(x^2 y\right)^{\frac{2}{3}}-\left(x y^2\right)^{\frac{2}{3}}=1$

If $A=\left[\begin{array}{cc}3 & 1 \\ -1 & 2\end{array}\right]$ show that $A^2-5 A+7 I_2=0$

Prove that $n^2-n$ divisible by 2 for every positive integer $n$

Construct a triangle similar to a given triangle LMN with its sides equal to $\frac{4}{5}$ of the corresponding sides of the triangle LMN (scale factor $\frac{4}{5}<1$ )

If nine times ninth term is equal to the fifteen times fifteenth term, show that six times twenty fourth term is zero

A(−3, 0) B(10, −2) and C(12, 3) are the vertices of ∆ABC. Find the equation of the altitude through A and B.

If $f(x)=x^2, g(x)=3 x$ and $h(x)=x-2$ Prove that (fog)oh $=f(goh)$

In a three-digit number, when the tens and the hundreds digit are interchanged the new number is 54 more than three times the original number. If 198 is added to the number, the digits are reversed. The tens digit exceeds the hundreds digit by twice as that of the tens digit exceeds the unit digit. Find the original number

In two concentric circles, a chord of length 16 cm of larger circle becomes a tangent to the smaller circle whose radius is 6 cm. Find the radius of the larger circle

Simplify $\frac{x^3-y^3}{3 x^2+9 x y+6 y^2} \times \frac{x^2+2 x y+y^2}{x^2-y^2}$