Consider the bases v₁ = (1,0)¹, v₂ = (0, 1) and v₁ = (2, 1), v₂ = (1,3)¹ of R². The transition matrix from the basis {V₁, V₂} to the basis {v₁, v₂} is

Help neeee in part a and B thanks in advance

Suppose A is the matrix for T: R3 - R3 relative to the standard basis. Find the diagonal matrix A' for T relative to the basis B'. -2 -1 A = 0 -1 B' = {(-1, 1, 0), (2, 1, 0), (0, 0, 1)} A' =

The coordinates for the vector v = (1,2,4) relative to the standard basis B = {(1,0,0), (0, 1,0), (0,0,1)} is [v] B = (1,2,4). The coordinates for v relative to the nonstandard basis B' = {(1, 0, -1), (2,1,-1), (-2, 1,4)} is [v]B¹ = (9,−1,3). Find the transition matrix P-1 from B to B' and show that this does change the coordinate of v relative to B to the coordinate of v relative to B'.

Find the change-of-coordinates matrix from B to the standard basis in R". 8 3 3 B= 7 -3 - 4 8 P8 =

I know the basis converted to orthogonal is {<2, 1, -1, 1>,<11, -12, 5, -5>,<-1, -3, 0, 5>} and that the magnitude of these will be sqrt(7), sqrt(315), sqrt(35) - but I'm not sure how to use these to convert the basis to orthonormal.

Explain how fixing a basis v1, · · , Vn of V associates to a quadratic form a corresponding function in n variables of the form q(x1,· . for a certain symmetric matrix A = (aj). , Xn) = Li=1 aijXiXj, .

Find the coordinate matrix of x in R" relative to the basis B. B' = {(8, 11, 0), (7, 0, 10), (1, 4, 6)), x = (-4, 19, -8) [x] = 000 11 It 7