-8
the dot product of two orthogonal vectors is Zero
a.b=0
<1,4>.<t,2>=0
t+8=0
t=-8
Question 5 Let a = (1,4) and b = {t,2). If a and b are orthogonal...
5. (a) Let u 1,4,2), ,1,0). Find the orthogonal projection of u on v (b) Letu ,1,0), u(0,1,1), (10,1). Find scalars c,,s such that 6. (a) Find the area of the triangle with vertices , (2,0,1), (3, 1,2). Find a vector orthogonal to the plane of the triangle. (b)) Find the distance between the point (1,5) and the line 2r -5y1 (i) Find the equation of the plane containing the points (1,2, 1), (2,1, 1), (1, 1,2). 7. (a) Let...
Question 4: [10pt total] Let ū = (1,4), T = (–7,5), and W = (-2, -1). Calculate the following: Q4)a) [2pt] 7 + V Q4)b) [2pt] 3 V Q4)c) [2pt] 27 – +3W Q4)d) [3pt] (-1,-1, 2) + (7,0,-5) – (2,8,0) = Q4)e) (3pt] (2a + 2b,b,c – a) – 2(a, a + b,c) =
full proofs for both and please write legibly 5. Let T be an orthogonal transformation on a finite dimensional vector space V over the real numbers, with an inner product. Show that D(T) = $1. 6. Show that if u,...,U, are orthonormal vectors in R, (see (15.7)), then D(uj, ..., Un) = 1.
a. Let B be an n x n Orthogonal matrix, that is B^-1 = B^T, and let A be an n x n skew-symmetric matrix. Simplify A(A^2(BA)^-1)^T b. Let A be a square matrix such that A^3 = 0. A is then called a nilpotent matrix. Define another matrix B by the expression B = I - A; Show that B is invertible and that its inverse is I + A + A^2 c. Let B = (-2,0,0 ; 0,0,0...
please explain this qustion. Let X ∼N(1,4) and g(t) = P(X > t), −∞< t <∞. (a) Find the value t that minimizes g(t+4)−g(t) and justify your answer. (b) Redo (a) for X ∼N(1,σ2). Does your answer depend on σ? Explain why.
#9 6.4.10 Question Help Find an orthogonal basis for the column space of the matrix to the right. - 1 co 5 -8 4 - 2 7 1 -4 -4 An orthogonal basis for the column space of the given matrix is O. (Type a vector or list of vectors. Use a comma to separate vectors as needed.)
(3 points) Let W be the subspace of R spanned by the vectors 1and 5 Find the matrix A of the orthogonal projection onto W A- (3 points) Let W be the subspace of R spanned by the vectors 1and 5 Find the matrix A of the orthogonal projection onto W A-
Find an orthogonal basis for the column space of the matrix to the right. -1 5 5 1 -7 4 1 - 1 7 1 -3 -4 An orthogonal basis for the column space of the given matrix is O. (Type a vector or list of vectors. Use a comma to separate vectors as needed.) The given set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal basis for 3 W. 6 -2 An...
3 5 Let y = and us .Write y as the sum of two orthogonal vectors, one in Span {u} and one orthogonal to u. 8 -5 y=y+z=]] (Type an integer or simplified fraction for each matrix element. List the terms in the same order as they appear in the original list.)
Let W be the subspace of R4 spanned by the orthogonal vectors 1 0 0 ui , ua : 0 1 Find the orthogonal decomposition of v = ܝܬ ܥ 5 -4 6 with respect to W. -5 p= projw (v) = q= perpw («) =