NCERT Class 12 Maths
Chapter 4: Determinants
18 Questions Solved
NCERT Solutions for Class 12 Maths Chapter 4 Determinants — Exercise 4.4
Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.
Question 1
Find the adjoint of \(\left[\begin{matrix}1 & 2\\3 & 4\end{matrix}\right]\).
Question 2
Find the adjoint of \(\left[\begin{matrix}1 & -1 & 2\\2 & 3 & 5\\-2 & 0 & 1\end{matrix}\right]\).
Question 3
Verify A(adj A)=(adj A)A=|A|I for A=\(\left[\begin{matrix}2 & 3\\-4 & -6\end{matrix}\right]\).
Question 4
Verify A(adj A)=(adj A)A=|A|I for A=\(\left[\begin{matrix}1 & -1 & 2\\3 & 0 & -2\\1 & 0 & 3\end{matrix}\right]\).
Question 5
Find the inverse, if it exists, of \(\left[\begin{matrix}2 & -2\\4 & 3\end{matrix}\right]\).
Question 6
Find the inverse, if it exists, of \(\left[\begin{matrix}-1 & 5\\-3 & 2\end{matrix}\right]\).
Question 7
Find the inverse, if it exists, of \(\left[\begin{matrix}1 & 2 & 3\\0 & 2 & 4\\0 & 0 & 5\end{matrix}\right]\).
Question 8
Find the inverse, if it exists, of \(\left[\begin{matrix}1 & 0 & 0\\3 & 3 & 0\\5 & 2 & -1\end{matrix}\right]\).
Question 9
Find the inverse, if it exists, of \(\left[\begin{matrix}2 & 1 & 3\\4 & -1 & 0\\-7 & 2 & 1\end{matrix}\right]\).
Question 10
Find the inverse, if it exists, of \(\left[\begin{matrix}1 & -1 & 2\\0 & 2 & -3\\3 & -2 & 4\end{matrix}\right]\).
Question 11
Find the inverse, if it exists, of \(\left[\begin{matrix}1 & 0 & 0\\0 & \cos{\left(\alpha \right)} & \sin{\left(\alpha \right)}\\0 &…
Question 12
For A = \(\left[\begin{matrix}3 & 7\\2 & 5\end{matrix}\right]\), B = \(\left[\begin{matrix}6 & 8\\7 & 9\end{matrix}\right]\), verify…
Question 13
For A=\(\left[\begin{matrix}3 & 1\\-1 & 2\end{matrix}\right]\), show A²−5A+7I=0 and hence find A⁻¹.
Question 14
For A=\(\left[\begin{matrix}3 & 2\\1 & 1\end{matrix}\right]\), find a,b such that A²+aA+bI=0.
Question 15
For A=\(\left[\begin{matrix}1 & 1 & 1\\1 & 2 & -3\\2 & -1 & 3\end{matrix}\right]\), show A³−6A²+5A+11I=0 and hence find A⁻¹.
Question 16
For A=\(\left[\begin{matrix}2 & -1 & 1\\-1 & 2 & -1\\1 & -1 & 2\end{matrix}\right]\), show A³−6A²+9A−4I=0 and hence find A⁻¹.
Question 17
If A is a nonsingular matrix of order 3, find |adj A|.
Question 18
If A is an invertible matrix of order 2, find |A⁻¹|.