Let A be a n×n matrix, then ( )
A:
AAT =ATA.
B:
det(AAT ) = det(AT A).
C:
if det(A) = 0, then A is invertible.
D:
if det(A) = 0, then AT is invertible.
A:
AAT =ATA.
B:
det(AAT ) = det(AT A).
C:
if det(A) = 0, then A is invertible.
D:
if det(A) = 0, then AT is invertible.
举一反三
- Let A be an m×n matrix, then ( ). A: AAT =ATA. B: if rank(A) = m, then AT A is invertible. C: if rank(A) = n, then AAT is invertible. D: if rank(A) = n, then AT A is invertible.
- If I-AB is invertible, then I-BA is invertible. Where I is the identity matrix, and A is m by n, B is n by m.
- 设矩阵A为n阶方阵，将其第t列的k倍加到第s列，得到矩阵B，则下面哪个选项是正确的？ A: det(B)=det(A) B: det(B)=-det(A) C: det(B)=det(-A) D: det(-B)=det(A)
- 3、若实方阵 A 满足（ ）时，则存在唯一单位下三角阵 L 和上三角阵 R ，使 A = LR 。 A: det A ¹ 0 B: 某个det Ak ¹ 0 C: det Ak ¹ 0 (k = 1,Ln -1) D: det Ak ¹ 0 (k = 1,L, n)
- det(AB)=det(A)det(B