1. Which of the following matrices is a square matrix?
Answer:
Explanation:
A square matrix has an equal number of rows and columns. Hence, a 4×4 matrix is a square matrix.
2. The order of the matrix [[1,2],[3,4],[5,6]] is:
Answer:
Explanation:
The matrix has 3 rows and 2 columns, so its order is 3×2.
3. If A is a matrix of order 2×3, then the total number of elements in matrix A is:
Answer:
Explanation:
For a matrix of order 2×3, there are 2 rows and 3 columns, so total elements = 2×3 = 6.
4. Two matrices are said to be equal if:
Answer:
Explanation:
Two matrices are equal if they have the same order and their corresponding elements are equal.
5. The zero matrix of order 2×2 is:
Answer:
Explanation:
A zero matrix has all its elements as zero.
6. If A and B are matrices of the same order, then (A+B)' is:
Answer:
Explanation:
The transpose of the sum of two matrices is the sum of their transposes.
7. The matrix [[1,2],[3,4]] is of type:
Answer:
Explanation:
The given matrix has equal numbers of rows and columns, making it a square matrix.
8. If A is a matrix of order 3×2, the order of its transpose A' is:
Answer:
Explanation:
The transpose of a matrix interchanges its rows with columns.
9. The matrix which has only one row is called:
Answer:
Explanation:
A matrix with a single row is termed a row matrix.
10. The sum of the diagonal elements of a matrix is called:
Answer:
Explanation:
The sum of the diagonal elements of a matrix is termed its trace.
11. The element situated in the third row and second column of the matrix [[1,2,3],[4,5,6],[7,8,9]] is:
Answer:
Explanation:
The element in the third row and second column is 8.
12. If A' is the transpose of A, then (A')' is:
Answer:
Explanation:
Taking the transpose twice results in the original matrix.
13. For any square matrix A, (A+A') is always:
Answer:
Explanation:
A matrix is symmetric if it is equal to its transpose.
14. A matrix in which all elements are zero except the diagonal elements is called:
Answer:
Explanation:
A matrix with non-zero elements only on its diagonal is a diagonal matrix.
15. If A is an identity matrix of order 3×3, then the sum of all its elements is:
Answer:
Explanation:
The identity matrix has ones on the diagonal and zeros elsewhere.
16. A square matrix in which all the elements below its main diagonal are zero is called:
Answer:
Explanation:
An upper triangular matrix has all elements below the diagonal as zero.
17. If A and B are matrices of order 3×3, then the order of the product matrix AB is:
Answer:
Explanation:
The product of two matrices has the order of the first matrix's rows by the second matrix's columns.
18. The number of rows in a column matrix of order 7×1 is:
Answer:
Explanation:
A column matrix has a single column, and in this case, 7 rows.
19. If two matrices A and B are conformable for multiplication, then:
Answer:
Explanation:
For two matrices to be conformable for multiplication, the number of columns in the first matrix must equal the number of rows in the second matrix.
20. If a matrix has only one column, it is called:
Answer:
Explanation:
A matrix with a single column is termed a column matrix.