Unit 6: Matrices and determinants - Practice Quiz

1 A matrix that has an equal number of rows and columns is called a:

2 A matrix in which all elements are zero is known as a:

3 The order of the matrix is:

4 A diagonal matrix in which all the diagonal elements are equal to is called a:

5 If and , then is:

6 Two matrices can be added only if they have the same:

7 If , then the transpose is:

8 If , then equals:

9 The product of two matrices is defined only when the number of columns of equals the number of:

10 The determinant of is:

11 The value of is:

12 If the determinant of a square matrix is zero, the matrix is called:

13 The determinant of the identity matrix is:

14 For , the adjoint of is:

15 The inverse of a matrix is given by the formula:

16 A matrix has an inverse only if it is:

17 If , then is:

18 A system of linear equations can be solved using the inverse matrix as:

19 To solve the system using the inverse method, the coefficient matrix must be:

20 In Cramer's rule for two equations, the value of is given by , where Cramer's rule fails when:

21 If a square matrix satisfies and all its diagonal elements are equal to a constant while all off-diagonal elements are zero, then is best described as a:

22 For which value of is the matrix skew-symmetric?

23 If and , then equals:

24 If and , then the product is:

25 For matrices and that are conformable for multiplication, which property is always true for the transpose of a product?

26 If is a matrix and is a matrix, what is the order of the product ?

27 The value of the determinant is:

28 Evaluate the determinant .

29 For what value of is the matrix singular?

30 The value of the determinant is:

31 If , then the adjoint of is:

32 The inverse of is:

33 For a non-singular square matrix of order , the relationship equals:

34 If for a matrix , then equals:

35 The system , is written as . What is the coefficient matrix ?

36 For the matrix equation where is non-singular, the solution is given by:

37 Using the matrix inverse method, solve , . The solution is:

38 By Cramer's rule for , , the value of is given by , where is:

39 Using Cramer's rule, solve , . The value of is:

40 In Cramer's rule, if the determinant of the coefficient matrix equals zero while at least one of or is non-zero, then the system:

41 If is a skew-symmetric matrix of order , then the value of is

42 A matrix is called involutory if . Which of the following matrices is involutory?

43 If and , then equals

44 If is a matrix and is a matrix, what is the order of ?

45 The value of is

46 If , then the determinant obtained by multiplying every element of the second row by and then interchanging the first and third rows equals

47 The matrix is singular for

48 The adjoint of is

49 The inverse of is

50 If is a non-singular matrix with , then equals

51 If is a matrix with , then equals

52 The inverse of is

53 Using the matrix inverse method, the solution of is

54 For the system , the value of obtained by Cramer's rule is

55 The system fails to have a unique solution when

56 If , then equals

57 The symmetric part of , given by , is

58 If is , is , and is , then the order of is

59 If and are matrices with and , then equals

60 If is a matrix with , then equals