Matrices
ICSE · Class 12 · Mathematics
Flashcards for Matrices — ICSE Class 12 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Get startedFind 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:…
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 …
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.
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.
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]].
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…
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]].
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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