NCERT Class 12 · Ch 4 Exercise 4.4 · Q4
NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.4 Question 4
Verify A(adj A)=(adj A)A=|A|I for A=\(\left[\begin{matrix}1 & -1 & 2\\3 & 0 & -2\\1 & 0 & 3\end{matrix}\right]\).
💡 Concept Hints
- Identify whether this needs determinant expansion, an inverse, or the absolute determinant formula for area.
- For a determinant use signed cofactors. For a system first check invertibility; for an area take half the absolute determinant.
✅ Step-by-Step Solution
Final Answer: \(\left[\begin{matrix}11 & 0 & 0\\0 & 11 & 0\\0 & 0 & 11\end{matrix}\right]\)
- The cofactor matrix is \(\left[\begin{matrix}0 & -11 & 0\\3 & 1 & -1\\2 & 8 & 3\end{matrix}\right]\); transpose it to get adj A=\(\left[\begin{matrix}0 & 3 & 2\\-11 & 1 & 8\\0 & -1 & 3\end{matrix}\right]\).
- The determinant is \(11\).
- Both products A(adj A) and (adj A)A evaluate to \(\left[\begin{matrix}11 & 0 & 0\\0 & 11 & 0\\0 & 0 & 11\end{matrix}\right]\), which is det(A)I.
Master Chapter 4: Determinants
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Determinants.
← Previous Question
Verify A(adj A)=(adj A)A=|A|I for A=\(\left[\begin{matrix}2 & 3\\-4…
Next Question →Find the inverse, if it exists, of \(\left[\begin{matrix}2 & -2\\4 &…
Related Questions in Determinants
Class 12 Determinants · Mcq Single Correct
If \(\begin{vmatrix}2 & 4\\5 & 1\end{vmatrix}\)=\(\begin{vmatrix}2x & 4\\6 &…
Class 12 Determinants · Mcq Single Correct
The area of the triangle with vertices (−3,0),(3,0),(0,k) is 9 square units. Find k.
Class 12 Determinants · Mcq Single Correct
Let f(x)=\(\begin{vmatrix}0 & x−a & x−b\\x+a & 0 & x−c\\x+b & x+c & 0\end{vmatrix}\). Which…
Class 12 Determinants · Mcq Single Correct
If \(\begin{vmatrix}2 & 3 & 2\\x & x & x\\4 & 9 & 1\end{vmatrix}\)+3=0, find x.
Class 12 Determinants · Mcq Single Correct
If x=−4 is a root of \(\begin{vmatrix}x & 2 & 3\\1 & x & 1\\3 & 2 & x\end{vmatrix}\)=0, find…
Class 12 Determinants · Mcq Single Correct
For a 3×3 real matrix A, det(Aᵀ)=−3. Find det(AAᵀ).