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Matrices — Flashcards

ICSE · Class 12 · Mathematics

32 flashcards for Matrices (ICSE Class 12 Mathematics) to test yourself on key terms and facts. Sample: "Find the order and number of elements"

97 questions32 flashcards18 formulas & key relations5 concepts

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A visual representation of a matrix, clearly showing its elements, rows, columns, and how its order (m x n) is defined. Highlight the 'a_ij' notation for elements.
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One of 11 illustrations for Matrices in Super Tutor — alongside flashcards, concept maps and practice questions.

32 Flashcards·
Order of a matrixMatrix countingEqual matricesMatrix additionMatrix subtractionScalar multiplication
Card 1Order of a matrix

Find the order and number of elements of the matrix A = [[2, 5, 19, -7], [35, -2, 5/2, 12], [sqrt(3), 1, -5, 17]].

Answer

Step 1: Count rows = 3 and columns = 4. Step 2: Order = 3 x 4. Step 3: Number of elements = 3 x 4 = 12. Step 4: The elements include 19 in a13, 35 in a21, -5 in a33, 12 in a24, and 5/2 in a23. Answer:…

Card 2Order of a matrix

A matrix has 18 elements. What are all possible orders?

Answer

Step 1: The number of elements in an m x n matrix is mn. Step 2: Factor 18. Step 3: 18 = 1 x 18 = 18 x 1 = 2 x 9 = 9 x 2 = 3 x 6 = 6 x 3. Answer: Possible orders are 1 x 18, 18 x 1, 2 x 9, 9 x 2, 3 x …

Card 3Matrix counting

How many matrices of order 3 x 3 are possible if each entry is 0 or 1?

Answer

Step 1: A 3 x 3 matrix has 9 entries. Step 2: Each entry has 2 choices: 0 or 1. Step 3: Total matrices = 2^9. Step 4: 2^9 = 512. Answer: 512 matrices.

Card 4Equal matrices

Given A = [[4, 3], [x, 5]] and B = [[y, z], [1, 5]], find x, y, and z if A = B.

Answer

Step 1: Equal matrices have the same order and equal corresponding entries. Step 2: Compare entries: 4 = y 3 = z x = 1 5 = 5 Step 3: Solve directly. Answer: x = 1, y = 4, z = 3.

Card 5Matrix addition

Solve: [[1, -1], [2, 0]] + [[4, -1], [1, -2]].

Answer

Step 1: Add corresponding entries. Step 2: First row: 1 + 4 = 5, and -1 + (-1) = -2. Step 3: Second row: 2 + 1 = 3, and 0 + (-2) = -2. Answer: [[5, -2], [3, -2]].

Card 6Matrix addition

Why is A + B not defined when A and B are of different orders?

Answer

Step 1: Matrix addition is entrywise. Step 2: Each entry of A must match exactly one corresponding entry of B. Step 3: If the numbers of rows or columns differ, some entries have no pair. Example: a 2…

Card 7Matrix subtraction

Find A - B if A = [[-1, 0], [3, 9]] and B = [[3, 2], [-1, 7]].

Answer

Step 1: Subtract corresponding entries. Step 2: First row: -1 - 3 = -4, and 0 - 2 = -2. Step 3: Second row: 3 - (-1) = 4, and 9 - 7 = 2. Answer: [[-4, -2], [4, 2]].

Card 8Scalar multiplication

Find 3A if A = [[-1, 0], [3, 9]].

Answer

Step 1: Multiply every entry by 3. Step 2: 3(-1) = -3, 3(0) = 0, 3(3) = 9, 3(9) = 27. Answer: 3A = [[-3, 0], [9, 27]].

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Frequently Asked Questions

What are the important topics in Matrices for ICSE Class 12 Mathematics?
Key topics in Matrices include Basic concepts and types of matrices, Equality, addition, subtraction, and scalar multiplication, Multiplication of matrices and matrix polynomials, Transpose of a matrix. Study these first, then practise questions on each for the ICSE Class 12 board exam.
How many flashcards are available for Matrices?
There are 32 flashcards for Matrices covering key definitions, facts and ideas. A few sample cards are shown on this page.
How should I revise Matrices for the ICSE Class 12 board exam?
Learn the core ideas first, then work through the 97 practice questions on Matrices. Revise definitions regularly and use flashcards for quick recall before the exam.

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Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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