True/False Chapter 3

Question 1

An nxn determinant is defined by determinants of (n-1)x(n-1) submatrices

Answer 1

true

Question 2

The (i,j)-cofactor of a matrix A is the matrix Aij obtained by deleting from A its ith row and jth column

Answer 2

false

Question 3

The cofactor expansion of det A down a column is equal to the cofactor expansion along a row

Answer 3

false

Question 4

The determinant of a triangular matrix is the sum of the entries on the main diagonal

Answer 4

false

Question 5

A row replacement operation does not affect the determinant of a matrix

Answer 5

true

Question 6

The determinant of A is the product of the pivots in any echelon form U of A, multiplied by (-1)^r, where r is the number of row interchanges made during row reduction from A to U

Answer 6

true

Question 7

If the columns of A are linearly independent, then det A = 0

Answer 7

true

Question 8

det (A + B) = det A + det B

Answer 8

false

Question 9

If three row interchanges are made in succession, then the new determinant equals the old determinant

Answer 9

true

Question 10

The determinant of A is the product of the diagonal entries in A

Answer 10

false

Question 11

If det A is zero, then two rows or two columns are the same, or a row or a column is zero

Answer 11

false

Question 12

det A^-1 = (-1) det A

Answer 12

false