Linear Algebra T&F CH. 2

For all square matrices A and B, it is true that det(A +B) = det(A + B)

False

If A is a 3x3 matrix and B is obtained from A by adding 5 times the first row to each of the second and thirds rows, then det(B) = 25det(A)

False

If A is a 3x3 matrix, then det(2A)=2det(A)

False

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

False

Two square matrices that have the same determinant must have the same size

False

For every 2x2 matrix A it is true that det(A^2) = (det(A))^2

True

For every nxn matrix A, we have A*adj(A)=(det(A))Isubn

True

If A and B are square matrices of the same size and A is invertible, then det(A^-1BA)=det(B)

True

If A is a 4x4 matrix and B is obtained from A by interchanging the first two rows and then interchanging the last two rows, then det(B) = det(A)

True

If A is a square matrix and the linear system Ax=0 has multiple solutions for x, then det(A)=0

True

If A is a square matrix whose minors are all zero, then det(A) = 0

True

If A is a square matrix with two identical columns, then det(A)=0

True

If A is invertible, then adj(A) must also be invertible

True

If E is an elementary matrix, then Ex=0 has only the trivial solution

True

If the sum of the second and fourth row vectors of a 6x6 matrix is equal to the last row vector, then det(A)=0

True

The number obtained by a cofactor expansion of a matrix A is independent of the row or column chosen for the expansion

True