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NCERT Class 12 Maths Chapter 3: Matrices 12 Questions Solved

NCERT Solutions for Class 12 Maths Chapter 3 Matrices — Exercise 3.3

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

Find the transposes of (1) \(\left[\begin{matrix}5\\1\\2\\-1\end{matrix}\right]\); (2) \(\left[\begin{matrix}1 & -1\\2 &…

A=\(\left[\begin{matrix}-1 & 2 & 3\\5 & 7 & 9\\-2 & 1 & 1\end{matrix}\right]\), B=\(\left[\begin{matrix}-4 & 1 & -5\\1 & 2 & 0\\1 & 3…

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

Given Aᵀ=\(\left[\begin{matrix}-2 & 3\\1 & 2\end{matrix}\right]\) and B=\(\left[\begin{matrix}-1 & 0\\1 & 2\end{matrix}\right]\)…

Verify (AB)ᵀ=BᵀAᵀ for (1) A = \(\left[\begin{matrix}1\\-4\\3\end{matrix}\right]\), B = \(\left[\begin{matrix}-1 & 2 &…

Verify AᵀA=I for (1) A=\(\left[\begin{matrix}\cos{\left(\alpha \right)} & \sin{\left(\alpha \right)}\\- \sin{\left(\alpha \right)} &…

Show (i) A=\(\left[\begin{matrix}1 & -1 & 5\\-1 & 2 & 1\\5 & 1 & 3\end{matrix}\right]\) is symmetric; (ii) B=\(\left[\begin{matrix}0…

For A=\(\left[\begin{matrix}1 & 5\\6 & 7\end{matrix}\right]\), verify (i) A+Aᵀ is symmetric; (ii) A−Aᵀ is skew symmetric.

Find (A+Aᵀ)/2 and (A−Aᵀ)/2 for A=\(\left[\begin{matrix}0 & a & b\\- a & 0 & c\\- b & - c & 0\end{matrix}\right]\).

Express each as the sum of symmetric and skew-symmetric matrices: (1) \(\left[\begin{matrix}3 & 5\\1 & -1\end{matrix}\right]\); (2)…

If A,B are symmetric matrices of the same order, which property must AB−BA have?

For A=\(\left[\begin{matrix}\cos{\left(\alpha \right)} & - \sin{\left(\alpha \right)}\\\sin{\left(\alpha \right)} & \cos{\left(\alpha…