ECAT Mathematics — Matrices and Determinants
Matrices and Determinants is part of the Mathematics section of the UET ECAT (30 of the 100 MCQs). It breaks into 5 subtopics, and we hold 49 ECAT-pattern practice MCQs on it, each with a written explanation. Tap a subtopic below to practise just that.
Subtopics (5)
How Matrices and Determinants is tested
Across the 7 ECAT past papers on ParhaiKrlo, Matrices and Determinants accounts for 19 questions. It appears in all 7, about 2.7 questions a paper. The heaviest was ECAT Past Paper 04, with 6 questions, and the most recent is ECAT Past Paper 07, with 2.
| Paper | Questions |
|---|---|
| ECAT Past Paper 07 | 2 |
| ECAT Past Paper 06 | 4 |
| ECAT Past Paper 05 | 1 |
| ECAT Past Paper 04 | 6 |
| ECAT Past Paper 03 | 2 |
| ECAT Past Paper 02 | 3 |
| ECAT Past Paper 01 | 1 |
Matrices and Determinants MCQs from the ECAT past papers
Try each one before opening the answer. Each comes with a short explanation.
- Q1 · ECAT Past Paper 07 · Matrices and Determinants
The reduced row echelon form of the augmented matrix of a linear system is [1 0 0 | 0; 0 2 −1 | 3; 0 0 0 | 1]. The system has:
- A.No solution
- B.Exactly one solution
- C.Two solutions
- D.Infinitely many solutions
Show answer
Answer: A. No solution — The last row reads 0 = 1, which is impossible.
- Q2 · ECAT Past Paper 06 · Matrices and Determinants
A = [3 −4; 2 −2] and B = [27; 16]. Given that AX = B, the matrix X = ?
- A.[−3; 5]
- B.[−2; 5]
- C.[5; −3]
- D.[5; 3]
Show answer
Answer: C. [5; −3] — |A| = 2; X = A⁻¹B = ½[−2 4; −2 3][27; 16] = ½[10; −6] = [5; −3].
- Q3 · ECAT Past Paper 05 · Matrices and Determinants
If A = [0 0; 0 p], then the value of p for which A + A⁻¹ = KI is:
- A.1, 2
- B.−1, 2
- C.Not valid for any value
- D.0, 1
Show answer
Answer: C. Not valid for any value — |A| = 0 for every p (the first row is zero), so A⁻¹ never exists.