Linear Algebra Problem 4: Given the normal vector n - 2 determine the matrix of the projection linear map through the plane (passing through the origin) which has n as a normal vector. Problem 5: Give...
4. Let S be a plane in R3 passing through the origin, so that S is a two- dimensional subspace of R3. Say that a linear transformation T: R3 R3 is a reflection about Sif T(U) = v for any vector v in S and T(n) = -n whenever n is perpendicular to S. Let T be the linear transformation given by T(x) = Ar, 1 1 А -2 2 2 21 -2 2 3 T is a reflection about...
Linear algebra Problem 5. Determine uhether the given vector is in the span of s. 12 1(14.01.1tt
Bycalculatingthecharacteristicpolynomial,eigenvaluesanddimensionsoftheeigenspaces of each map or matrix below, determine if the given map or matrix is diagonalizable. If a map or matrix is diagonalizable, diagonalize it (linear algebra) 1. By calculating the characteristic polynomial, eigenvalues and dimensions of the eigenspaces of each map or matrix below, determine if the given map or matrix is diagonalizable. If a map or matrix is diagonalizable, diagonalize it (that is, give a basis consisting of its eigenvectors) The field F over which you consider the...
Find parametric equations of the plane that passes through the origin and has normal vector (3, 1, −6).
4) Find the standard matrix for RRR given by reflection through the plane y mz (mER). Hint: if we restrict R to the ry-plane, it reduces to T from problem (1). 4) Find the standard matrix for RRR given by reflection through the plane y mz (mER). Hint: if we restrict R to the ry-plane, it reduces to T from problem (1).
linear algebra Determine the augmented matrix A# of the given system. W + 2 2x + 2x – – - y y 3y + + + 5z = 7 = 132 3, -5, 8. 4w
3)Find the angle between the plane 2x-6z + 5= 0 and the line passing through 2 points (1, 1, 1) and (-2, 1, 4). Hint, the angle between a line and a plane is the angle between direction vector of the line and the normal vector of the plane.
linear algebra please show work and steps 16. Determine if the vector = an D= (2 2 is a linear combination of the vectors: u; - and uz = 11 17. Determine if the vector 5 = 8 is in the span of the columns of the matrix. A = 5 112) Ecos 2 6 10 3 7 11) 19 18. Determine if the sets of vectors -5 are linearly independent. If the sets are linearly dependent, find a dependence...
Problem 1: Denote by Ruo to be the linear map R3 k, IR3 which rotates points around the vector by the right-hand rule, by an angle of θ. Determine the matrix Rk el. Problem 2: Let p be the point (1,2,3) E R3. (i) Rotate p around 1 by an angle θ-| then rotate around j by ψ = 증. (ii) Rotate p around j by then rotate around i by Problem 1: Denote by Ruo to be the linear...