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NCERT Class 12 Maths Chapter 3: Matrices 22 Questions Solved

NCERT Solutions for Class 12 Maths Chapter 3 Matrices — Exercise 3.2

Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.

Let A = \(\left[\begin{matrix}2 & 4\\3 & 2\end{matrix}\right]\), B = \(\left[\begin{matrix}1 & 3\\-2 & 5\end{matrix}\right]\), C =…

Compute: (1) \(\left[\begin{matrix}a & b\\- b & a\end{matrix}\right]\) + \(\left[\begin{matrix}a & b\\b & a\end{matrix}\right]\); (2)…

Compute: (1) \(\left[\begin{matrix}a & b\\- b & a\end{matrix}\right]\) \(\left[\begin{matrix}a & - b\\b & a\end{matrix}\right]\); (2)…

For A = \(\left[\begin{matrix}1 & 2 & -3\\5 & 0 & 2\\1 & -1 & 1\end{matrix}\right]\), B = \(\left[\begin{matrix}3 & -1 & 2\\4 & 2 &…

For A = \(\left[\begin{matrix}\frac{2}{3} & 1 & \frac{5}{3}\\\frac{1}{3} & \frac{2}{3} & \frac{4}{3}\\\frac{7}{3} & 2 &…

Simplify \(\cos{\left(\theta \right)}\) \(\left[\begin{matrix}\cos{\left(\theta \right)} & \sin{\left(\theta \right)}\\…

Find X,Y for (i) X+Y=\(\left[\begin{matrix}7 & 0\\2 & 5\end{matrix}\right]\), X−Y=\(\left[\begin{matrix}3 & 0\\0 &…

Given Y=\(\left[\begin{matrix}3 & 2\\1 & 4\end{matrix}\right]\) and 2X+Y=\(\left[\begin{matrix}1 & 0\\-3 & 2\end{matrix}\right]\)…

Find x,y if 2\(\left[\begin{matrix}1 & 3\\0 & x\end{matrix}\right]\) + \(\left[\begin{matrix}y & 0\\1 & 2\end{matrix}\right]\) =…

Solve for x,y,z,t in 2\(\left[\begin{matrix}x & z\\y & t\end{matrix}\right]\) +3\(\left[\begin{matrix}1 & -1\\0 &…

Solve x\(\left[\begin{matrix}2\\3\end{matrix}\right]\) +y\(\left[\begin{matrix}-1\\1\end{matrix}\right]\) =…

Find x,y,z,w if 3\(\left[\begin{matrix}x & y\\z & w\end{matrix}\right]\) = \(\left[\begin{matrix}x & 6\\-1 & 2 w\end{matrix}\right]\)…

For F(x)=\(\left[\begin{matrix}\cos{\left(x \right)} & - \sin{\left(x \right)} & 0\\\sin{\left(x \right)} & \cos{\left(x \right)} &…

Show AB≠BA for (1) A = \(\left[\begin{matrix}5 & -1\\6 & 7\end{matrix}\right]\), B = \(\left[\begin{matrix}2 & 1\\3 &…

For A=\(\left[\begin{matrix}2 & 0 & 1\\2 & 1 & 3\\1 & -1 & 0\end{matrix}\right]\), compute A²−5A+6I.

For A=\(\left[\begin{matrix}1 & 0 & 2\\0 & 2 & 1\\2 & 0 & 3\end{matrix}\right]\), prove A³−6A²+7A+2I=O.

Find k so that A²=kA−2I for A=\(\left[\begin{matrix}3 & -2\\4 & -2\end{matrix}\right]\).

For A=\(\left[\begin{matrix}0 & - \tan{\left(\frac{\alpha}{2} \right)}\\\tan{\left(\frac{\alpha}{2} \right)} &…

A ₹30000 trust fund is split between bonds paying fixed annual rates of 5% and 7%. Using matrix multiplication, find allocations for…

A bookshop has 10 dozen chemistry, 8 dozen physics and 10 dozen economics books, sold at ₹80,₹60,₹40 each. Find total receipts using…

Let X,Y,Z,W,P have orders 2×n,3×k,2×p,n×3,p×k respectively. What restrictions make PY+WY defined?

For X of order 2×n and Z of order 2×p with n=p, what is the order of 7X−5Z?