Linear Algebra Answers

Determine if the matrix p=
D= 1/√2, 0, 1/√2
0, 1, 0
-1/√2, 2, 1/√2
Is othognal.

Show that no skew symmetric matrix can be of rank 1

Q. Find the dimension of the subspace of R4 that is span of the vectors
(█(1¦(-1)@0@1)), (█(2¦1@1@1)),(█(0¦0@0@0)),(█(1¦1@-2@-5))

|2 3 7 |
If |1 x -2 | = 5, find x.
|0 2 x |

Q. Find the dimension of the subspace of R4 that is span of the vectors
(█(1¦(-1)@0@1)), (█(2¦1@1@1)),(█(0¦0@0@0)),(█(1¦1@-2@-5))

Choose the correct answer.
Q. If F is a linear transformation from R2 to R and F(1,1)=2, F(1,0)=3, then F(2,3)=?
a. 3
b. 2
c. 1
d. -4

Choose the correct answer.
Q. Let A be an m×n matrix, then which of the following is true.
a. Rank(A)≤m, Nulity(A)≥n
b. Rank(A)≤min(m,n), Nulity(A)≥n-min(m,n)
c. Rank(A)≤m, Nulity(A)≥n-max(m,n)
d. Rank(A)≤m, Nulity(A) ≤n-max(m,n )

Choose the correct answer.
Q.If M and N are 3 dimensional subspaces of R^6, then what is possible dimension of subspace M∩N?
a. 2,3,4,6
b. 1,2,3,4
c. 0,1,2,3
d. 3,4,5,6

Reduce the following equation to standard form hence identify the conic it represents x2 - 3xy + y2 + 4x - 4y - 5 = 0

The form x2 + y2 + z2 and x2 - y2 - z2 are equivalent. True or false