Quiz about 0B2 Wk6 Tutorial MCQs (Determinants)

Question 1

What is the determinant of A?

Accepted Answer

28

Answer

-44

Answer

-36

Answer

44

Question 2

Which of the formulae in the picture is the formula for calculating the determinant of a 3x3 matrix?

Accepted Answer

b

Answer

a

Answer

c

Answer

d

Question 3

The $$\left(i,j ight)-th$$ minor $$A_{ij}$$ of an $$n imes n$$ matrix $$A$$ is... (select the correct statement)

Accepted Answer

d) The determinant of the matrix obtained by deleting the i-th row and j-th column of A.

Answer

a) Another name for the (i,j)-th entry of A.

Answer

b) The matrix obtained by deleting the i-th row and j-th column of A.

Answer

c) The matrix obtained by deleting the j-th row and i-th column of A.

Question 4

Suppose a square matrix B is obtained by swapping rows $$s$$ and $$t$$ $$\left(s e t ight)$$ of another square matrix A. Which of the following are true?

Accepted Answer

a) $$\det\left(B\right)=-\det\left(A\right)$$

Answer

b) $$\det\left(B\right)=s\det\left(A\right)$$

Answer

c) $$\det\left(B\right)=\det\left(A\right)$$

Answer

d) $$t\det\left(B\right)=\det\left(A\right)$$

Question 5

Suppose a square matrix B is obtained by multiplying row $$s$$ of another square matrix A by some non-zero scalar $$\mu$$ . Which of the following are true?

Accepted Answer

b) $$\det\left(B\right)=\mu\det\left(A\right)$$

Answer

a) $$\det\left(B\right)=-\det\left(A\right)$$

Answer

c) $$\det\left(B\right)=\det\left(A\right)$$

Answer

d) $$\mu\det\left(B\right)=\det\left(A\right)$$

Question 6

Suppose $$U$$ is an $$n imes n$$ matrix in row echelon form. Which of the following can be used to calculate $$\det\ U$$ ?

Accepted Answer

d) $$\det\ U=u_{11}u_{22}...u_{nn}$$

Answer

a) $$\det\ U=u_{11}u_{12}...u_{1n}$$

Answer

b) $$\det\ U=u_{n1}u_{n2}...u_{nn}$$

Answer

c) $$\det\ U=u_{1n}u_{2n}...u_{nn}$$

Question 7

Suppose $$A$$ is an $$n imes n$$ matrix such that $$\det\ A e0$$ . Which of the following are also true?

Accepted Answer

a) $$A$$ can be reduced to a matrix in REF which does not have a zero row.

Accepted Answer

c) $$A$$ is invertible

Accepted Answer

d) Any system of linear equations whose LHS is represented by $$A$$ has a unique solution.

Answer

b) $$A$$ can be reduced to the zero matrix i.e. the $$n imes n$$ matrix whose every entry is 0.

Question 8

Suppose $$A$$ is an invertible $$n imes n$$ . Which of the following are also true?

Accepted Answer

a) $$A$$ can be reduced to a matrix in REF which does not have a zero row.

Accepted Answer

c) $$\det A e0$$ .

Accepted Answer

d) Any system of linear equations whose LHS is represented by $$A$$ has a unique solution.

Answer

b) $$A$$ can be reduced to the zero matrix i.e. the $$n imes n$$ matrix whose every entry is 0.

Question 9

What is the determinant of A?

Accepted Answer

-12

Answer

0

Answer

12

Answer

18

Answer

-18

0B2 Wk6 Tutorial MCQs (Determinants)

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