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Matrices and Determinants Operations Quiz

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Matrices and Determinants Operations Quiz

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Questions and Answers

What is the multiplicative identity of a matrix?

A matrix whose elements are all zeros except the diagonal elements which are ones (correct)

A matrix whose elements are all ones

A matrix whose determinant is equal to one

A matrix whose determinant is equal to zero

If A and B are square matrices, which of the following statements is true?

(AB)^-1 = A^-1B^-1

(AB)^-1 = B^-1A

(AB)^-1 = BA^-1

(AB)^-1 = B^-1A^-1 (correct)

What is the determinant of a square matrix?

A scalar value associated with a matrix that represents the volume of the parallelotope formed by its row vectors

A scalar value associated with a matrix that represents the area of the parallelogram formed by its row vectors

A scalar value associated with a matrix that represents the scaling factor of the linear transformation represented by the matrix (correct)

A scalar value associated with a matrix that represents the sum of the diagonal elements of the matrix

What is a singular matrix?

Both (a) and (c) are correct Signup and view all the answers

What is the adjoint of a matrix?

The matrix obtained by replacing each element by its cofactor Signup and view all the answers

Which method can be used to solve a system of two linear equations with two unknowns?

Both (a) and (b) can be used Signup and view all the answers

What is the order of a matrix A with m rows and n columns?

m-by-n Signup and view all the answers

When are two matrices A and B considered equal?

If they have the same number of rows and columns, and their corresponding elements are equal. Signup and view all the answers

What is the order of the matrix $A = \begin{bmatrix} 1 \end{bmatrix}$?

1-by-1 Signup and view all the answers

What is the order of the matrix $B = \begin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix}$?

2-by-2 Signup and view all the answers

What is the order of the matrix $C = \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \end{bmatrix}$?

2-by-3 Signup and view all the answers

What is the order of the matrix $D = \begin{bmatrix} 1 \ 2 \ 3 \end{bmatrix}$?

3-by-1 Signup and view all the answers