Matrices — Class 12 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 12 Mathematics chapter "Matrices" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 12 Mathematics chapter "Matrices" — 8 important questions with detailed answers for CBSE board exam prepar…
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Key Questions Covered:
- Find x and y if [x+y, 2y] = [7, 8].
- If A = [1 2; 3 4] and B = [2 0; 1 3], find A + B.
- If A = [1 2 3; 4 5 6] and k = 2, find kA.
- + 5 more questions in the full chapter
Solutions Summary:
| Question | Status |
|---|---|
| Find x and y if [x+y, 2y] = [7, 8]. | ✓ Solved |
| If A = [1 2; 3 4] and B = [2 0; 1 3], find A + B. | ✓ Solved |
| If A = [1 2 3; 4 5 6] and k = 2, find kA. | ✓ Solved |
Showing 3 of 8 questions
Q1: Find x and y if [x+y, 2y] = [7, 8].
Given: [x + y, 2y] = [7, 8]
Two matrices (or arrays) are equal if and only if their corresponding elements are equal.
Comparing corresponding elements:
First element: x + y = 7 ... (1)
Second element: 2y = 8 ... (2)
From equation (2):
2y = 8
y = 4
Substituting y = 4 into equation (1):
x + 4 = 7
...
Q2: If A = [1 2; 3 4] and B = [2 0; 1 3], find A + B.
Given: A = [1 2; 3 4] and B = [2 0; 1 3]
To find A + B, add corresponding elements:
A + B = [1 2; 3 4] + [2 0; 1 3]
= [1+2, 2+0; 3+1, 4+3]
= [3, 2; 4, 7]
CONCLUSION: A + B = [3 2; 4 7]
Q3: If A = [1 2 3; 4 5 6] and k = 2, find kA.
Given: A = [1 2 3; 4 5 6] and k = 2
Scalar multiplication of a matrix is performed by multiplying each element by the scalar:
kA = 2 × [1 2 3; 4 5 6]
= [2×1, 2×2, 2×3; 2×4, 2×5, 2×6]
= [2, 4, 6; 8, 10, 12]
CONCLUSION: kA = [2 4 6; 8 10 12]
Showing 3 of 8 questions. Visit the full page for complete solutions.