Download App

Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices4 Marks
Question
If $A=\left[\begin{array}{cc}3 & a \\ -4 & 8\end{array}\right], B=\left[\begin{array}{cc}c & 4 \\ -3 & 0\end{array}\right], C=\left[\begin{array}{cc}-1 & 4 \\ 3 & b\end{array}\right]$ and $3 A -2 C =6 B$, find the values of $a, b, c$.
✓

Answer

$3A - 2C = 6B$
$\begin{array}{l}3\left[\begin{array}{cc}3 & a \\ -4 & 8\end{array}\right]-2\left[\begin{array}{cc}-1 & 4 \\ 3 & b\end{array}\right]=6\left[\begin{array}{cc}c & 4 \\ -3 & 0\end{array}\right] \end{array} $
$ {\left[\begin{array}{cc}9 & 3 a \\ -12 & 24\end{array}\right]-\left[\begin{array}{cc}-2 & 8 \\ 6 & 2 b\end{array}\right]=\left[\begin{array}{cc}6 c & 24 \\ -18 & 0\end{array}\right]} $
$ {\left[\begin{array}{cc}11 & 3 a-8 \\ -18 & 24-2 b\end{array}\right]=\left[\begin{array}{cc}6 c & 24 \\ -18 & 0\end{array}\right]}$
Comparing the corresponding elements we get
$3 a-8=24 $
$\Rightarrow 3 a=32 $
$\Rightarrow a=\frac{32}{3}=10 \frac{2}{3}$
$24-2 b=0 $
$\Rightarrow 2 b=24$
$\Rightarrow b=12$
$11=6 c $
$\Rightarrow c=\frac{11}{6}=1 \frac{5}{6}$
 

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 "[4 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

If $a, b, c$ and $d$ are in proportion, prove that:
$
\frac{a^2+a b}{c^2+c d}=\frac{b^2-2 a b}{d^2-2 c d}
$
→
Attempt this question on a graph paper. The table shows the distribution of marks gained by a group of $400$ students in an examination.
Marks (Less than ) 10 20 30 40 50 60 70 80 90 100
No.of student 5 10 30 60 105 180 270 355 390 400
Using scaie of $2cm$ to represent $10$ marks and $2 cm$ to represent $50$ student, plot these point and draw a smooth curve though the point
Estimate from the graph :
(1)the median marks
(2)the quartile marks.
→
Solve the following equation and give your answer up to two decimal places:
$x^2 - 5x - 10 = 0$
→
In a cyclic-trapezium, the non-parallel sides are equal and the diagonals are also equal. Prove it.
→
From the following cumulative frequency table , find :
Median
Lower quartile
Upper quaetile
 
Marks (less than ) 10 20 30 40 50 60 70 80 90 100
Cumulative frequency 5 24 37 40 42 48 70 77 79 80
→
If $\frac{ a }{ b }=\frac{ c }{ d }$, show that: $\frac{a^3 c+a c^3}{b^3 d+b d^3}=\frac{( a + c )^4}{( b + d )^4}$
→
An aeroplane flying with a wind of 30 km/hr takes 40 minutes less to fly 3600 km, than what it would have taken to fly against the same wind. Find the planes speed of flying in still air.
→
Solve : $2\left(\frac{x}{x+1}\right)^2-5\left(\frac{x}{x+1}\right)+2=0, x \neq-1$
→
The points $A, B$ and $C$ are $(4, 0), (2, 2)$ and $(0, 6)$ respectively. Find the equations of $AB$ and
$BC$. If $AB$ cuts the y-axis at P and BC cuts the x-axis at $Q$, Find the co-ordinates of $P$ and $Q.$
→
Solve the following inequation and represent the solution set on the number line:
$4 x-19<\frac{3 x}{5}-2 \leq \frac{-2}{5} x \in R$
→