1)For all u, v E R^3, we have u . (u x v) = 0 2)For all vectors x.docx

1. 1)For all u, v E R^3, we have u . (u x v) = 0
2)For all vectors x, y E R^2, we have proj x = proj y?
3)If there are more variables than equations in a system of
linear equations, then there can NOT be a unique solution to the
system?
4)If the m x n matrix A is a row equivalent to B, then Row
(A)=Row (B)?
5)If A and B are upper triangulr matrices, then A+B is an upper
triangular matrix?
6)If A, B and C are all n x n matrices, and if AB=AC, then
B=C?
7)If A is an invertible matrix, then rank (A ^-1)=1/rank(A)?
8)[1 0 2pi]
[0 1 0] is an elementary matrix?
[0 0 1]
9)Suppose that A is an n x n matrix and that B i obtained from
a by adding r times the first row of A to the second row of A.
Then det B= r det A?
10)Suppose that A is an invertible matrix. Then A^T is also
invertible, and (A^T)^-1=(A^-1)^T?
Solution
1) False
2) True
3) True