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

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

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

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

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

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?

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

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

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

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

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

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

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

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

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

Suppose $$A$$ is an $$n\times n$$ matrix such that $$\det\ A\ne0$$ . Which of the following are also true?

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

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

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

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

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

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

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

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MULTIPLE CHOICE QUESTION

1 min • 1 pt

What is the determinant of A?

-44

-36

MULTIPLE CHOICE QUESTION

45 sec • 1 pt

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

MULTIPLE SELECT QUESTION

45 sec • 1 pt

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

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

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

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

MULTIPLE CHOICE QUESTION

45 sec • 1 pt

MULTIPLE CHOICE QUESTION

45 sec • 1 pt

MULTIPLE SELECT QUESTION

1 min • 1 pt

MULTIPLE SELECT QUESTION

1 min • 1 pt

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