Let V be a vector space with dim(V)=3. Suppose A={ v
​
1
​
, v
​
2
​
, v
​
3
​
, v
​
4
​
, v
​
5
​
}⊆V What can we deduce about A ? Select one: A. It must be linearly dependent, but may or may not span V It may or may not be linearly independent, and may or may not span V. c. It must be linearly dependent and will span V D. It must be linearly independent, but cannot span V E. It can span V, but only if it is linearly independent, and vice versa The orthogonal projection of v 1
​
onto v 2
​
is ( ∥v 2
​
∥ 2
v 1
​
⋅v 2
​
​
)v 2
​
Let a= ⎝
⎛
​
1
1
1
​
⎠
⎞
​
onto b= ⎝
⎛
​
0
1
−2
​
⎠
⎞
​
The orthogonal projection of a onto b is w. w T
equals Select one: A. (0,−1/3,2/3) в. (−1/3,−1/3,1/3) c. (1/3,−1/3,1/3) D. (−1/3,−1/3,−1/3) Which of the following is/are TRUE for invertible n×n matrices A and B ? I II III ​
:det(AB)=det(A)det(B)
:det(A −1
)=[det(A)] −1
:det(AB)=det(BA)
​
Matrix A is A=( 1
k
​
1
k
​
). Given that A 2
=0, where 0 is the zero matrix, what is the value of k ? Select one: A. −1 B. 0 C. −2 D. 2 E. 1