Midterm 3 Flashcards
1
Q
Nul A where A is a 4×5 matrix, n=4
A
No
2
Q
Col B where B is a 6 × 4 matrix, n = 4.
A
No
3
Q
Every list of n distinct vectors in Rn forms a basis of Rn
A
False
4
Q
If two rows of an n×n matrix A are equal, then det(A)=0
A
True
5
Q
If A is a 6×6 matrix, then det(−A)=det(AT)
A
True
6
Q
The rank of a matrix A is equal to the number of non-pivot columns of A.
A
False
7
Q
For every pair of 2 × 2 matrices A and B we have det(A − B) = det A − det B.
A
False
8
Q
For every n × n matrix A we have det A = − det(AT ).
A
False
9
Q
If an n × n matrix A is invertible then Nul A = {0}.
A
True
10
Q
If A is a 3×3 matrix such that two of its columns are equal, then we have det A = 0.
A
True
11
Q
The dimension of Nul A is always equal to the number of pivot columns of A.
A
False
12
Q
The columns of an invertible n × n matrix form a basis of Rn
A
True
