Download App

Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices3 Marks
Question
Find the matrix $X$ of order $2 \times 2$ which satisfies the equation $\left[\begin{array}{ll}3 & 7 \\ 2 & 4\end{array}\right]\left[\begin{array}{ll}0 & 2 \\ 5 & 3\end{array}\right]+2 X =\left[\begin{array}{cc}1 & -5 \\ -4 & 6\end{array}\right]$
✓

Answer

$\begin{aligned} & \text { Given } \\ & {\left[\begin{array}{ll}3 & 7 \\ 2 & 4\end{array}\right]\left[\begin{array}{ll}0 & 2 \\ 5 & 3\end{array}\right]+2 X =\left[\begin{array}{cc}1 & -5 \\ -4 & 6\end{array}\right]} \\ & \Rightarrow\left[\begin{array}{ll}0+35 & 6+21 \\ 0+20 & 4+12\end{array}\right]+2 X =\left[\begin{array}{cc}1 & -5 \\ -4 & 6\end{array}\right] \\ & \Rightarrow\left[\begin{array}{ll}35 & 27 \\ 20 & 16\end{array}\right]+2 X =\left[\begin{array}{cc}1 & -5 \\ -4 & 6\end{array}\right] \\ & 2 X =-\left[\begin{array}{ll}35 & 27 \\ 20 & 16\end{array}\right]+\left[\begin{array}{cc}1 & -5 \\ -4 & 6\end{array}\right] \\ & =\left[\begin{array}{ll}-34 & -32 \\ -24 & -10\end{array}\right] \\ & X =\frac{1}{2}\left[\begin{array}{ll}-34 & -32 \\ -24 & -10\end{array}\right] \\ & =\left[\begin{array}{cc}-17 & -16 \\ -12 & -5\end{array}\right] .\end{aligned}$

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

Ritu has a Recurring Deposit Account in a bank and deposits $Rs.80$ per month for $18$ months. Find the rate of interest paid by the bank if the maturity value of the account is $Rs.1,554.$
→
Prove.$\frac{1}{\sec A+\tan A}=\sec A-\tan A$
→
If $(2 x+1)$ is a factor of $6 x^3+5 x^2+a x-2$ find the value of $a$
→
What quantity must be subtracted from each term of the ratio $39 : 89$ to make it equal to $2 : 5 ?$
→
A doorway is decorated as shown in the figure. There are four semi-circles. $BC,$ the diameter of the larger semi-circle is of length $84\  cm.$ Centres of the three equal semicircles lie on $BC. ABC$ is an isosceles triangle with $AB = AC.$ If $BO = OC,$ find the area of the shaded region. (Take $\left.\pi=\frac{22}{7}\right)$
→
From a well shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn will:   be a face card.
→
If $A =\left[\begin{array}{ll}3 & 3 \\ p & q\end{array}\right]$ and $A ^2=0$ find $p$ and $q$
→
The fifth, eight and eleventh terms of a geometric progression are p, q and r respectively. show that : $q^2 = pr$.
→
Using remainder theorem, find the value of $k$ if on dividing $2 x^3+3 x^2-k x+5$ by $(x-2)$, leaves a remainder 7.
→
If the$ n^{th}$​​​​​​​ term of the $A.P. 58, 60, 62,....$ is equal to the $n^{th}​​​​​​​$​​​​​​​ term of the $A.P. -2, 5, 12, ….,$ find the value of n.
→