a

b

c

d

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.

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

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

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

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

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

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

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

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

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

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

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

c) $$A$$   is invertible

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

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

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

c) $$\det A\ne0$$  .

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

0

12

18

-12

-18