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Determinants — Flashcards

ICSE · Class 12 · Mathematics

30 flashcards for Determinants (ICSE Class 12 Mathematics) to test yourself on key terms and facts. Sample: "Evaluate the determinant: |A| for A = [[x"

100 questions30 flashcards20 formulas & key relations5 concepts

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A visual representation defining a determinant as a scalar value associated with a square matrix, showing its notation and basic structure.
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30 Flashcards·
Determinant of order 2Trigonometric determinantDeterminant of order 3Equation using determinantsMinorCofactorLaplace expansionCofactor expansion
Card 1Determinant of order 2

Evaluate the determinant: |A| for A = [[x, x+1], [x-1, x]].

Answer

Step 1: Use the 2x2 formula |A| = a11a22 - a21a12. Step 2: |A| = x·x - (x-1)(x+1). Step 3: |A| = x^2 - (x^2 - 1). Step 4: |A| = 1. Answer: 1…

Card 2Trigonometric determinant

Evaluate: [[cos 15°, sin 15°], [sin 75°, cos 75°]].

Answer

Step 1: Use |A| = a11a22 - a21a12. Step 2: |A| = cos 15°·cos 75° - sin 15°·sin 75°. Step 3: Use cos(A+B) = cos A cos B - sin A sin B. Step 4: |A| = cos(15° + 75°) = cos 90°. Step 5: cos 90° = 0. Answe…

Card 3Determinant of order 3

Evaluate the determinant: [[2, -1, -2], [0, 2, -1], [3, -5, 0]].

Answer

Step 1: Expand along the first row. Step 2: |A| = 2[(2)(0) - (-5)(-1)] - (-1)[(0)(0) - (3)(-1)] + (-2)[(0)(-5) - (3)(2)]. Step 3: |A| = 2(0 - 5) + 1(0 + 3) - 2(0 - 6). Step 4: |A| = -10 + 3 + 12. Step…

Card 4Equation using determinants

Find the value of x if [[2, 4], [5, 1]] = [[2x, 4], [6, x]].

Answer

Step 1: Find the determinant of both sides. Step 2: Left side = 2·1 - 5·4 = 2 - 20 = -18. Step 3: Right side = (2x)(x) - 6·4 = 2x^2 - 24. Step 4: Set equal: 2x^2 - 24 = -18. Step 5: 2x^2 = 6. Step 6: …

Card 5Minor

Find the minors of the elements of [[1, -2], [4, 3]].

Answer

Step 1: Delete the row and column of each element. Step 2: M11 = 3. Step 3: M12 = 4. Step 4: M21 = -2. Step 5: M22 = 1. Answer: M11 = 3, M12 = 4, M21 = -2, M22 = 1…

Card 6Cofactor

Find the cofactors of the elements of [[1, -2], [4, 3]].

Answer

Step 1: Use Cij = (-1)^(i+j) Mij. Step 2: C11 = (+1)(3) = 3. Step 3: C12 = (-1)(4) = -4. Step 4: C21 = (-1)(-2) = 2. Step 5: C22 = (+1)(1) = 1. Answer: C11 = 3, C12 = -4, C21 = 2, C22 = 1…

Card 7Laplace expansion

Why is the determinant equal to the sum of elements of any row multiplied by their cofactors?

Answer

This is Laplace expansion. For a row or column, |A| = sum of products of elements with corresponding cofactors. Example for a 2x2 matrix [[a, b], [c, d]]: |A| = aC11 + bC12 = a(d) + b(-c) = ad - bc. S…

Card 8Cofactor expansion

Using cofactors of the first column, evaluate [[4, 1], [-3, 2]].

Answer

Step 1: First column elements are 4 and -3. Step 2: C11 = 2. Step 3: C21 = -1. Step 4: |A| = 4·2 + (-3)(-1). Step 5: |A| = 8 + 3 = 11. Answer: 11…

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Frequently Asked Questions

What are the important topics in Determinants for ICSE Class 12 Mathematics?
Key topics in Determinants include Basic Idea of Determinants, Minors and Cofactors, Important Determinant Properties, Adjoint of a Matrix. Study these first, then practise questions on each for the ICSE Class 12 board exam.
How many flashcards are available for Determinants?
There are 30 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 ICSE Class 12 board exam?
Learn the core ideas first, then work through the 100 practice questions on Determinants. Revise definitions regularly and use flashcards for quick recall before the exam.

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