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Determinants — Flashcards

Madhya Pradesh Board · Class 12 · Mathematics

48 flashcards for Determinants (Madhya Pradesh Board Class 12 Mathematics) to test yourself on key terms and facts.

111 questions48 flashcards15 formulas & key relations5 concepts

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An illustration showing a triangle with its vertices labeled, alongside the determinant formula used to calculate its area.
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48 Flashcards·
Determinant of order 2क्रम 2 का निर्धारकEquating determinantsनिर्धारकों का समीकरण3x3 सारणिक विस्तार3x3 determinant expansion
Card 1Determinant of order 2

Evaluate 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…

Card 2क्रम 2 का निर्धारक

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…

Card 3क्रम 2 का निर्धारक

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…

Card 4Determinant of order 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…

Card 5Equating determinants

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…

Card 6निर्धारकों का समीकरण

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 =…

Card 73x3 सारणिक विस्तार

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…

Card 83x3 determinant expansion

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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Frequently Asked Questions

What are the important topics in Determinants for Madhya Pradesh Board Class 12 Mathematics?
Key topics in Determinants include Basics of Determinants, Expansion of a 3 × 3 Determinant, Determinant Properties and Special Results, Adjoint and Inverse of a Matrix. Study these first, then practise questions on each for the Madhya Pradesh Board Class 12 board exam.
How many flashcards are available for Determinants?
There are 48 flashcards for Determinants covering key definitions, facts and ideas. A few sample cards are shown on this page.
How should I revise Determinants for the Madhya Pradesh Board Class 12 board exam?
Learn the core ideas first, then work through the 111 practice questions on Determinants. Revise definitions regularly and use flashcards for quick recall before the exam.

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