1)USE row operations to and triangular form to compute the determinant of the ma

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 invertibleD=2)true or false1)For all u v E R^3 we have u . (u x v) = 02)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 setT= {[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 31a) Find the BASIS FOR THE NULLSPACE OF A1B)BASIS FOR ROWSPACE OF A1C) COLUMNSPACE OF A.