1)USE row operations to and triangular form to compute the determinant of the matrix D givn below, AND determine all values of p such that D is invertible

D=

[ 3 2 5 p]

[0 1 -3 9]

[0 1 4 2]

[1 1 1 1]

2)true or false

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?

3)Showif the set

T= {[1 2] , [1 2] , [1 -3]

[1 -1] [3 1] [2 1]}

is Linearly dependent orlinearlyindependent.?

4)The matrix A=

1 2 3 -1 -6

-2 -4 -5 4 -1

-1 -2 0 2 -8

-3 -6 -4 3 3

1a) Find the BASIS FOR THE NULLSPACE OF A,

1B)BASIS FOR ROWSPACE OF A,

1C) COLUMNSPACE OF A.