Free Simultaneous Equations and Matrices MCQs with Answers
30 Simultaneous Equations and Matrices MCQs from Quantitative Methods, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.
Simultaneous equations are solved by substitution, elimination and comparison, including systems with two or three unknowns. Matrices cover order, equality, addition, multiplication, determinants, inverses and solving equations by matrix methods, with attention to the difference between matrix multiplication and ordinary number multiplication.
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30 questions · page 2 of 2
- A. 1
- B. 2
- C. 3
- D. 4
Explanation: From the second equation, y = 3x - 3. Substituting this into the first equation gives x = 2 and therefore y = 3.
Correct answer: 3- A. 6
- B. 8
- C. 10
- D. 12
Explanation: The required entry is obtained by multiplying the second row of A by the first column of B: (3 × 0) + (4 × 2) = 8.
Correct answer: 8- A. [[0, 0], [0, 0]]
- B. [[1, 1], [1, 1]]
- C. [[1, 0], [0, 1]]
- D. [[0, 1], [1, 0]]
Explanation: The 2 × 2 identity matrix has ones on the main diagonal and zeros elsewhere.
Correct answer: [[1, 0], [0, 1]]- A. -3
- B. -1
- C. 3
- D. 5
Explanation: Expanding along the first row gives 2(3 × 1 - 2 × 2) - 1(1 × 1 - 2 × 0) = -3. Therefore, the determinant is -3.
Correct answer: -3- A. rank(A) = 1 and rank([A|B]) = 1
- B. rank(A) = 2 and rank([A|B]) = 3
- C. rank(A) = 3 and rank([A|B]) = 2
- D. rank(A) = 2 and rank([A|B]) = 2
Explanation: A unique solution requires the rank of the coefficient matrix to equal the rank of the augmented matrix and to equal the number of…
Correct answer: rank(A) = 2 and rank([A|B]) = 2- A. [[2, 1], [2, 1]]
- B. [[3, 1], [2, 2]]
- C. [[2, 2], [1, 1]]
- D. [[4, 2], [4, 2]]
Explanation: Subtract the identity matrix from the right side to obtain [[4, 2], [4, 2]], then divide every entry by 2. This gives X = [[2, 1], [2, 1]].
Correct answer: [[2, 1], [2, 1]]- A. 1/(ad-bc) [[a, -b], [-c, d]]
- B. 1/(ad-bc) [[d, -b], [-c, a]]
- C. 1/(ad+bc) [[d, b], [c, a]]
- D. 1/(ad-bc) [[-d, b], [c, -a]]
Explanation: The inverse is found by interchanging a and d, changing the signs of b and c, and dividing by the determinant ad - bc.
Correct answer: 1/(ad-bc) [[d, -b], [-c, a]]- A. Replace the second column with the constants
- B. Add the two coefficient columns
- C. Replace the first column with the constants
- D. Multiply both coefficient columns by the constants
Explanation: To calculate x with Cramer's rule, replace the coefficient column belonging to x with the constants column.
Correct answer: Replace the first column with the constants- A. It has only the zero solution
- B. It has no solution
- C. It always has exactly two solutions
- D. It has infinitely many solutions
Explanation: A homogeneous system is always consistent because the zero vector is a solution.
Correct answer: It has infinitely many solutions- A. To make every entry equal to one
- B. To reveal pivots and simplify back-substitution
- C. To change a rectangular matrix into a square matrix
- D. To calculate the transpose without multiplication
Explanation: Row-echelon form places the matrix in a triangular pattern that clearly shows pivot positions and free variables.
Correct answer: To reveal pivots and simplify back-substitution