Matrices
Punjab Board · Class 12 · Mathematics
Flashcards for Matrices — Punjab Board Class 12 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Get startedFind the order of matrix A = [[2, 5, 19, -7], [35, -2, 5/2, 12], [√3, 1, -5, 17]]
Answer
Step 1: Count the number of rows = 3 Step 2: Count the number of columns = 4 Step 3: Order of matrix = m × n = 3 × 4 Answer: The matrix A is of order 3 × 4 (read as 3 by 4)…
If a matrix has 24 elements, what are all possible orders it can have?
Answer
Step 1: If matrix has order m × n, then total elements = m × n = 24 Step 2: Find all factor pairs of 24: - 1 × 24 - 24 × 1 - 2 × 12 - 12 × 2 - 3 × 8 - 8 × 3 - 4 × 6 - 6 × 4 Answer: Po…
Construct a 2 × 2 matrix A = [aᵢⱼ] where aᵢⱼ = (i + j)²/2
Answer
Step 1: Set up general form: A = [[a₁₁, a₁₂], [a₂₁, a₂₂]] Step 2: Calculate each element: - a₁₁ = (1 + 1)²/2 = 4/2 = 2 - a₁₂ = (1 + 2)²/2 = 9/2 - a₂₁ = (2 + 1)²/2 = 9/2 - a₂₂ = (2 + 2)²/2 = 1…
When do you use matrix equality? Find x, y, z if [[4, 3], [x, 5]] = [[y, z], [1, 5]]
Answer
When: Use matrix equality when two matrices have the same order and you need to find unknown elements by comparing corresponding positions. Method: For A = B, we must have aᵢⱼ = bᵢⱼ for all i and j …
Identify the type of each matrix: (i) [5, 1/2, -1] (ii) [[4]] (iii) [[3, 0], [0, 3]]
Answer
Step 1: Analyze matrix (i) = [5, 1/2, -1] - Has 1 row and 3 columns - Type: ROW MATRIX (order 1 × 3) Step 2: Analyze matrix (ii) = [[4]] - Has 1 row and 1 column - Type: SQUARE MATRIX of orde…
Add matrices: A = [[√3, 1, -1], [2, 3, 0]] and B = [[2, √5, 1], [-2, 3, 1/2]]
Answer
Step 1: Check orders - both are 2 × 3, so addition is defined Step 2: Add corresponding elements - (1,1): √3 + 2 - (1,2): 1 + √5 - (1,3): -1 + 1 = 0 - (2,1): 2 + (-2) = 0 - (2,2): 3 + 3 = 6 …
Subtract and simplify: Find A - B where A = [[8, 0], [4, -2], [3, 6]] and B = [[2, -2], [4, 2], [-5, 1]]
Answer
Step 1: Verify both matrices have same order (3 × 2) ✓ Step 2: Subtract corresponding elements: A - B = [[a₁₁ - b₁₁, a₁₂ - b₁₂], [a₂₁ - b₂₁, a₂₂ - b₂₂], [a₃₁ - b₃₁, a₃₂ - b₃₂]]…
When do you use scalar multiplication of matrices? Compute 3A where A = [[3, 1, 1.5], [√5, 7, -3], [2, 0, 5]]
Answer
When: Multiply a matrix by a scalar (constant) to scale all elements. Used in: adjusting units, magnification, and solving matrix equations. Method: Multiply each element by the scalar k Step 1: Mul…
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