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Systems of Equations and Matrices — High School Pre-Calculus practice questions

12 multiple-choice questions and 5 flashcards on Systems of Equations and Matrices, about 8% of the High School Pre-Calculus bank. Every one carries a written rationale.

Written and maintained by the CoStudy team · last updated 2026-10-02 · how we write and review questions

What this chapter covers

Systems of Equations and Matrices is one of 10 chapters in CoStudy's High School Pre-Calculus bank, and it holds 12 of the bank's 150 multiple-choice questions — roughly 8% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.

Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.

Free Systems of Equations and Matrices practice questions

3 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.

Solve: x + y = 10 and x − y = 2.

  1. (4, 6)
  2. (6, 4)
  3. (5, 5)
  4. (8, 2)

Answer: B — (6, 4)

B) Correct — Add the equations: 2x = 12. A) Swaps x and y. C) Satisfies only the first equation. D) Satisfies only the first equation.

A = [[1, 2], [3, 4]] and B = [[2, 0], [1, 1]]. Find AB.

  1. [[4, 2], [10, 4]]
  2. [[2, 0], [3, 4]]
  3. [[2, 4], [4, 6]]
  4. [[3, 2], [4, 5]]

Answer: A — [[4, 2], [10, 4]]

A) Correct — Rows of A times columns of B: [1·2 + 2·1, 1·0 + 2·1; 3·2 + 4·1, 3·0 + 4·1]. B) Multiplies matching entries, which is not matrix multiplication. C) Computes BA; matrix multiplication is not commutative. D) Adds the matrices.

If AX = B and A is invertible, then X equals:

  1. A⁻¹B
  2. BA⁻¹
  3. B/A
  4. A⁻¹ + B

Answer: A — A⁻¹B

A) Correct — Multiply both sides on the left by A⁻¹. B) Multiplies on the wrong side; order matters. C) Matrix division is not defined. D) Adds instead of multiplying.

Systems of Equations and Matrices flashcards

3 cards from the 5 in this chapter.

What is the inverse of a 2×2 matrix [[a,b],[c,d]]?

(1/det) · [[d, −b], [−c, a]], where det = ad − bc.

When is a matrix invertible?

When its determinant is nonzero.

What is a matrix?

A rectangular array of numbers arranged in rows and columns. Used for linear systems, transformations, and more.

Practise the full chapter

These are a sample. The full Systems of Equations and Matrices chapter runs 17 items with per-chapter progress tracking, on the web and in the iOS app.

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