Determinants — Class 12 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 12 Mathematics chapter "Determinants" — 7 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 12 Mathematics chapter "Determinants" — 7 important questions with detailed answers for CBSE board exam pr…
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Key Questions Covered:
- Find the determinant of the matrix A = [2 3; 1 4].
- Find the determinant of B = [1 2 3; 0 4 5; 1 0 2].
- If A = [3 2; 1 4], find |2A| (the determinant of 2A).
- + 4 more questions in the full chapter
Solutions Summary:
| Question | Status |
|---|---|
| Find the determinant of the matrix A = [2 3; 1 4]. | ✓ Solved |
| Find the determinant of B = [1 2 3; 0 4 5; 1 0 2]. | ✓ Solved |
| If A = [3 2; 1 4], find |2A| (the determinant of 2A). | ✓ Solved |
Showing 3 of 7 questions
Q1: Find the determinant of the matrix A = [2 3; 1 4].
Given: A = [2 3; 1 4]
For a 2×2 matrix [a b; c d], the determinant is ad - bc.
Here: a = 2, b = 3, c = 1, d = 4
det(A) = (2)(4) - (3)(1)
= 8 - 3
= 5
CONCLUSION: det(A) = 5
Q2: Find the determinant of B = [1 2 3; 0 4 5; 1 0 2].
Given: B = [1 2 3; 0 4 5; 1 0 2]
We use expansion along the first column (since it has a zero):
det(B) = 1 × |4 5; 0 2| - 0 × |2 3; 0 2| + 1 × |2 3; 4 5|
Calculating the 2×2 determinants:
|4 5; 0 2| = (4)(2) - (5)(0) = 8 - 0 = 8
|2 3; 4 5| = (2)(5) - (3)(4) = 10 - 12 = -2
det(B) = 1(8) - 0 + 1(-...
Q3: If A = [3 2; 1 4], find |2A| (the determinant of 2A).
Given: A = [3 2; 1 4]
First, find 2A:
2A = [6 4; 2 8]
Now find det(2A):
det(2A) = (6)(8) - (4)(2)
= 48 - 8
= 40
ALTERNATIVE METHOD (using property):
For an n×n matrix A and scalar k: det(kA) = k^n × det(A)
Here n = 2 and k = 2.
First find det(A):
det(A) = (3)(4) - (2)(1) = 12 - 2...
Showing 3 of 7 questions. Visit the full page for complete solutions.