1. Math
  2. Advanced Math
  3. problem1 let b be a 4x4 matrix to which we...

Question: problem1 let b be a 4x4 matrix to which we...

Question details

Problem1 Let B be a 4x4 matrix to which we apply the following operations Double column 3 2. 1. Add row 2 to row 1 3. Interchange columns 2 and 3 4. Halve row 4 5. Each of these operations can be performed by multiplying B on the left or on the right by a specific matrix E (where k stands for the operation above) Find the matrices E. Then find matrices A and C such that the result is obtained as a product ABC Problem 2 Consider the matrix Replace column 4 by sum of columns 1 and 3 2 -1 2 Q2 2-1 Show that Q is an orthogonal matrix. What transformation of R does it correspond to? Hint: Find the vector a that is invariant under Q Pick a vector b orthogonal to a. Find the angle a between b and Qb. If this angle is independent of the choice of b, then O corresponds to a rotation about a by the angle a. Think about other possibilities.) Problem 3 Find the 2x2 orthogonal matrix Q that corresponds to the reflection over the line Problem 4 Let u, v be two vectors and A -1 + uv7 a matrix. Show that if A is invertible, its inverse is the matrix A-1-1 + αυντ and find the scalar α.When is A singular? Problem 5 (a) Compute the norms llw1, llw2,o for the vector w-1 (b) Compute the norms l|All1, lIA2Al for the matrix A - (c) verify the inequalities lA삐lp llAllpllwllp 2 -1 1 -1 0 2

Solution by an expert tutor
Blurred Solution
This question has been solved
Subscribe to see this solution