Chapter Exam

Chapter 3: Matrices — Online MCQ Test

Q: What is the order of a matrix with 4 rows and 5 columns?

Answer: A. 4 × 5 — The order of a matrix is represented as m × n, where m is the number of rows and n is the number of columns. Here, m=4 and n=5, so order is 4 × 5.

Q: Which of the following is a row matrix?

Answer: B. A matrix with 1 row and 3 columns — A row matrix contains only one row with multiple columns, so it has order 1 × n. A 1 × 3 matrix is a row matrix.

Q: If A is a 2 × 3 matrix and B is a 3 × 4 matrix, what is the order of AB?

Answer: A. 2 × 4 — For matrix multiplication AB to be defined, the number of columns in A must equal the number of rows in B (3 = 3, satisfied). The result has order m × p = 2 × 4.

Q: If matrix A has 5 elements and matrix B has 8 elements, can A + B be computed?

Answer: D. Cannot determine without knowing their orders — Matrix addition requires both matrices to have the same order. Knowing the number of elements alone is insufficient; for example, a 1 × 5 and 5 × 1 matrix both have 5 elements but different orders.

Q: Let A be a 3 × 3 matrix. If the sum of symmetric and skew-symmetric parts equals A, and the symmetric part is B = [[1, 2, 3], [2, 4, 5], [3, 5, 6]], what can we deduce?

Answer: D. All of the above — B represents the symmetric component, which is (A + A^T)/2 by definition. The skew-symmetric part is (A - A^T)/2. However, knowing B alone doesn't uniquely determine A; we need additional information.

MATHS · CLASS 12 INTER II YEAR · Andhra State Board

Practice Chapter 3: Matrices with a free chapter-wise online MCQ test for Andhra State Board CLASS 12 INTER II YEAR MATHS. This chapter covers: 1. Introduction and Basic DefinitionsDefinition: A matrix is an ordered rectangular array of numbers or functions, called elements or entries.Order of a Matrix: A matrix with m row.... AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter 3: Matrices — Important Questions & Answers (FAQ)

Frequently asked questions from Andhra State Board CLASS 12 INTER II YEAR MATHS — Chapter 3: Matrices, with answers and explanations. These are sample questions; the exam has its own separate question set.

What is the order of a matrix with 4 rows and 5 columns?

A. 4 × 5 ✓
B. 5 × 4
C. 9
D. 20

Answer: A. 4 × 5
The order of a matrix is represented as m × n, where m is the number of rows and n is the number of columns. Here, m=4 and n=5, so order is 4 × 5.

Which of the following is a row matrix?

A. A matrix with 3 rows and 1 column
B. A matrix with 1 row and 3 columns ✓
C. A matrix with 3 rows and 3 columns
D. A matrix with 0 rows

Answer: B. A matrix with 1 row and 3 columns
A row matrix contains only one row with multiple columns, so it has order 1 × n. A 1 × 3 matrix is a row matrix.

If A is a 2 × 3 matrix and B is a 3 × 4 matrix, what is the order of AB?

A. 2 × 4 ✓
B. 3 × 3
C. 2 × 3
D. Cannot be computed

Answer: A. 2 × 4
For matrix multiplication AB to be defined, the number of columns in A must equal the number of rows in B (3 = 3, satisfied). The result has order m × p = 2 × 4.

If matrix A has 5 elements and matrix B has 8 elements, can A + B be computed?

A. Yes, always
B. No, never
C. Only if both are row matrices
D. Cannot determine without knowing their orders ✓

Answer: D. Cannot determine without knowing their orders
Matrix addition requires both matrices to have the same order. Knowing the number of elements alone is insufficient; for example, a 1 × 5 and 5 × 1 matrix both have 5 elements but different orders.

Let A be a 3 × 3 matrix. If the sum of symmetric and skew-symmetric parts equals A, and the symmetric part is B = [[1, 2, 3], [2, 4, 5], [3, 5, 6]], what can we deduce?

A. B must be obtained from (A + A^T)/2
B. A cannot be uniquely determined from B alone
C. The skew-symmetric part is (A - A^T)/2
D. All of the above ✓

Answer: D. All of the above
B represents the symmetric component, which is (A + A^T)/2 by definition. The skew-symmetric part is (A - A^T)/2. However, knowing B alone doesn't uniquely determine A; we need additional information.