Chapter 3: Matrices — Online MCQ Test
MATHS · CLASS 12 SECOND PUC · Karnataka State Board
Practice Chapter 3: Matrices with a free chapter-wise online MCQ test.
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....
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Chapter 3: Matrices — Important Questions & Answers
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.
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.
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.
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.
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.
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.