Question

Determine if the statement is true or false, and justify your answer.

a. Every matrix A has a determinant.
b. Every nonsquare matrix has a determinant, but square matrices do not.
c. Every square matrix has a determinant, but nonsquare matrices do not.
d. If every entry in a matrix is zero, then the determinant is undefined.
e. If every entry in a matrix is one, then the determinant is undefined.

Answer 1

Explanation:

a) False. A rectangular matrix cannot have a determinant only square matrices can have determinants

b) False. Only square matrices have determinants and non square matrices do not have

c) True.

d) False. If it is a square matrix and every entry is 0 then determinant =0

e) False. If it is a square matrix determinant =0 since when two rows are identical the determinant value is 0.