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Flip to reveal answersHow do you state the order of a matrix?
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All 8 Flashcards — Introduction to matrices
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Question
How do you state the order of a matrix?
Answer
Rows × columns, rows first. E.g. 2 rows and 3 columns is a 2 × 3 matrix.
Question
When can two matrices be added?
Answer
Only when they have the same order; then you add matching entries.
Question
How do you scalar-multiply a matrix?
Answer
Multiply every entry by the scalar (e.g. 2A doubles each entry).
Question
When is the product AB defined, and what is its order?
Answer
When A's columns = B's rows (inner numbers match). The result is (rows of A) × (columns of B) — the outer numbers.
Question
How do you compute an entry of AB?
Answer
Slide along a row of A and down a column of B, multiply pair-by-pair, and add.
Question
What is the 2×2 identity matrix and what does it do?
Answer
I = ((1, 0), (0, 1)); AI = IA = A, so it leaves a matrix unchanged (like ×1).
Question
What is the determinant of A = ((a, b), (c, d))?
Answer
det A = ad − bc. If it equals 0, A has no inverse (singular).
Question
What is the inverse of A = ((a, b), (c, d))?
Answer
A⁻¹ = 1/(ad − bc) · ((d, −b), (−c, a)): swap diagonal, negate off-diagonal, divide by det.
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Topic 1.14 hub
Matrices (HL only)
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