Determinants
Madhya Pradesh Board · Class 12 · Mathematics
Flashcards for Determinants — Madhya Pradesh Board Class 12 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Explore the full setEvaluate the determinant: |2 4; -1 2|
Answer
Step 1: Use the 2x2 formula: |A| = a11 a22 - a12 a21. Step 2: Substitute values: |A| = (2)(2) - (4)(-1). Step 3: Calculate: 4 + 4 = 8. Answer: 8…
निर्णायक का मूल्यांकन करें: |2 4; -1 2|
Answer
चरण 1: 2x2 सूत्र का उपयोग करें: |A| = a11 a22 - a12 a21. चरण 2: मानों को प्रतिस्थापित करें: |A| = (2)(2) - (4)(-1). चरण 3: गणना करें: 4 + 4 = 8. उत्तर: 8…
निर्णायक का मूल्यांकन करें: |x x+1; x-1 1|
Answer
चरण 1: |A| = a11 a22 - a12 a21 का उपयोग करें। चरण 2: प्रतिस्थापित करें: |A| = x(1) - (x+1)(x-1)। चरण 3: विस्तार करें: x - (x^2 - 1) = x - x^2 + 1। उत्तर: 1 + x - x^2…
Evaluate the determinant: |x x+1; x-1 1|
Answer
Step 1: Use |A| = a11 a22 - a12 a21. Step 2: Substitute: |A| = x(1) - (x+1)(x-1). Step 3: Expand: x - (x^2 - 1) = x - x^2 + 1. Answer: 1 + x - x^2…
Solve for x: |3 x; x 1| = |3 2; 4 1|
Answer
Step 1: Evaluate each determinant. Left side: |3 x; x 1| = 3(1) - x(x) = 3 - x^2. Right side: |3 2; 4 1| = 3(1) - 2(4) = 3 - 8 = -5. Step 2: Equate: 3 - x^2 = -5. Step 3: x^2 = 8. Step 4: x = ±2√2. An…
x के लिए हल करें: |3 x; x 1| = |3 2; 4 1|
Answer
चरण 1: प्रत्येक सारणिक का मूल्यांकन करें। बायाँ पक्ष: |3 x; x 1| = 3(1) - x(x) = 3 - x^2. दायाँ पक्ष: |3 2; 4 1| = 3(1) - 2(4) = 3 - 8 = -5. चरण 2: बराबर करें: 3 - x^2 = -5. चरण 3: x^2 = 8. चरण 4: x =…
विस्तार का उपयोग करके निर्धारक का मूल्यांकन करें: Δ = |1 2 4; -1 3 0; 4 1 0|
Answer
चरण 1: तीसरे कॉलम में विस्तार करें क्योंकि इसमें दो शून्य हैं। चरण 2: Δ = 4 | -1 3; 4 1 | चरण 3: 2x2 सारणिक की गणना करें: (-1)(1) - (3)(4) = -1 - 12 = -13. चरण 4: 4 से गुणा करें: Δ = 4(-13) = -52. उत्…
Evaluate the determinant using expansion: Δ = |1 2 4; -1 3 0; 4 1 0|
Answer
Step 1: Expand along the third column because it has two zeros. Step 2: Δ = 4 | -1 3; 4 1 |. Step 3: Compute the 2x2 determinant: (-1)(1) - (3)(4) = -1 - 12 = -13. Step 4: Multiply by 4: Δ = 4(-13) = …
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