Download App

Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices3 Marks
Question
Find the value of p and q if:
$\left[\begin{array}{cc}2 p+1 & q^2-2 \\ 6 & 0\end{array}\right]=\left[\begin{array}{cc}p+3 & 3 q-4 \\ 5 q-q^2 & 0\end{array}\right]$.
✓

Answer

$2p + 1 = p + 3;$
$2p - p = 3 - 1$
$p = 2 ...(1)$
$q^2 - 2 = 3q - 4$
$q^2 - 3q + 2 = 0$
$q^2 - 2q - q + 2 = 0$
$q(q - 2) - (q - 2) = 0$
$(q - 2) (q - 1) = 0 ...(2)$
$5q - q^2 = 6$
$q^2 - 5q + 6 = 0$
$(q - 3) (q - 2) = 0 ...(3)$
By equation $(2)$ and $(3)$
$q = 2$
$\Rightarrow p = 2, q = 2.$

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 "[3 marks sum]" from Matrices→Matrices — all question types→Mathematics STD 10 question papers→ICSE Board STD 10 question papers→ICSE Board question paper generator→

Similar questions

Rs 50 shares of a company are quoted at a discount of 10%. Find the rate of dividend given by the company, the return on the investment on these shares being 20 per cent.
→
Calculate the Amount and Cornpound Interest for the Following, when Cornpounded Annually:
$Rs.12,000$ for $3$ years at $15\%$ p.a.
→
Show that $(x-1)$ is a factor of $x^3-5 x^2-x+5$ Hence factorise $x^3-5 x^2-x+5$.
→
Solve the equation and represent the solution set on the number line.
$-3+x \leq \frac{8 x}{3}+2 \leq \frac{14}{3}+2 x$, where $x \in I$
→
Five years ago, a woman’s age was the square of her son’s age. Ten years later her age will be twice that of her son’s age. Find:
The age of the son five years ago.
→
Find the 16th term of the A.P. $7,11,15,19$ $\qquad$ Also find the sum of the first 6 terms.
→
The speed of an express train is $x\ km/hr$ arid the speed of an ordinary train is $12\ km/hr$ less than that of the express train. If the ordinary train takes one hour longer than the express train to cover a distance of $240\ km,$ find the speed of the express train.
→
Solve and graph the solution set of:
$3x – 2 > 19$ or $3 – 2x \leq -7, x \in R$
→
A hollow sphere of internal and external radii $6\ cm$ and $8\ cm$ respectively is melted and recast into small cones of base radius $2\ cm$ and height $8\ cm.$ Find the number of cones.
→
Show that the points $A(1, 3), B(2, 6), C(5, 7)$ and $D(4, 4)$ are the vertices of a rhombus.
$=a\left(\frac{1}{t^2}+1\right)=\frac{a\left(t^2+1\right)}{t^2}$
$\text { Now } \frac{1}{ SP }+\frac{1}{ SQ }=\frac{1}{a\left(t^2+1\right)}+\frac{1 \times t^2}{a\left(t^2+1\right)}$
$=\frac{\left(1+t^2\right)}{a\left(t^2+1\right)}$
$\frac{1}{ SP }+\frac{1}{ SQ }=\frac{1}{a} .$
→