determine if v1= [ 2 1 0] v2=[ -1 1 3] v3=[ 0 -1 6] spans the vector space of rows with three real entries which has dimension 3. so I wanted to make sure I did this correct. First I created a matrix with v1,v2,v3 as the columns
Use a specific example to prove that the cross product is also not associative. That is, use three specific vectors in 3-space to show that Vector a×(Vector b × Vector c) is not equal to (Vector a × Vector b) × Vector c. Can
Use a specific example to prove that the cross product is also not associative. That is, use three specific vectors in 3-sapce to show that Vector a×(Vector b × Vector c) is not equal to (Vector a × Vector b) × Vector c.
a) If vector u and vector v are non-collinear vectors show that vector u, vector u cross product vector v and (vector u cross product vector v) cross product vector u are mutually othogonal. b) Verify this property using vectors
If A^TA is an invertible matrix, prove that the column vectors of A are linearly independent. You know that if statement X implies statement Y then that is equivalent to Not(Y) implies Not(X). You can start by taking the column
prove that normal to plane containing 3 points whose position vectors are a vector,b vector,c vectorlies in direction addition of cross product of vectors b and c and cross product of vectors c and a and cross product of vectors a
Find an orthonormal basis for the subspace of R^3 consisting of all vectors(a, b, c) such that a+b+c = 0. The subspace is two-dimensional, so you can solve the problem by finding one vector that satisfies the equation and then by
let vector U = (vector u1, vector u2) vector V = (vector v1, vector v2) and vector W = (vector w1, vector w2) Prove each property using Cartesian vectors: a) (vector U+V)+W = vector U+(v+W) b) k(vector U+V) = k vector U + k vector