Question: Prove: If O is an orthogonal matrix, then each entry of O is the same as its cofactor if det(Q) = 1 and is the

Prove: If O is an orthogonal matrix, then each entry of O is the same as its cofactor if det(Q) = 1 and is the negative of its cofactor if det (Q)= -1.

Step by Step Solution

★★★★★

3.54 Rating (164 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Let Q a ij be orthogonal Then ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

938-M-L-A-E (1352).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

(a) Show that if u Rn is a unit vector, then the n n matrix Q = 1 - 2uuT is an orthogonal matrix, known as an elementary reflection or Householder matrix. (b) Write down the elementary reflection...

Show that if AT = - A is any skew-symmetric matrix, then its Cayley Transform Q = (I - A)-1 (I + A) is an orthogonal matrix. Can you prove that I - A is always invertible?

Show that if A is an orthogonal matrix, then A-1 is orthogonal?

The Polar Decomposition: Prove that every invertible matrix A has a polar decomposition, written A = QB, into the product of an orthogonal matrix Q and a positive definite matrix B > 0. Show that if...

MATH-1250: Linear Algebra I 2021 Homework Assignment 7 Professor: Alfakih 1. Let S = span fr = (a) Use Gram-Schmidt process to find an orthogonal basis {u', u, u3} of S. (b) Find an orthonormal basis...

Can you please help me with this? And can you please explain the answers to me? Please do not use cursive as I can't read that. Let S = span fal - : -- - - [ : 1 (a) Use Gram-Schmidt process to find...

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

1. Let S = span {al (a) Use Gram-Schmidt process to find an orthogonal basis ful, u', u}} of S. (b) Find an orthonormal basis (q',93, q' } of S. 2. Let S = span fa = - - [ ;] (a) Use Gram-Schmidt...

chapter 5 INTRODUCTION TO MATRIX ALGEBRA GOALS The purpose of this chapter is to introduce you to matrix algebra, which has many applications. You are already familiar with several algebras:...

Discuss the criteria and the measure of performance used when items are sequenced on a production facility?

What is the difference (functional group) between ephedrine (in cold medicines) and methamphetamine (crystal meth)?

If the variable cost per unit decreases while the sales proe per unt and total feed costs remain constant, which of fie folowing statements is trie? A . The contribution margin decreapes and the...

Suppose you are the Chief Executive Officer of a large German company, who is considering erecting a manufacturing facility in the United States and selling either inside the United States or...

Let A and B be n n matrices. (a) Show that AB = O if and only if the column space of B is a subspace of the null space of A. (b) Show that if AB = O, then the sum of the ranks of A and B cannot...

Let A Rmn, b Rm, and let x0 be a particular solution to the system Ax = b. Prove the following. A vector y in Rn will be a solution to Ax = b if and only if y = x0 + z, where z N(A). If N(A) =...

Let x and y be nonzero vectors in Rm and Rn, respectively, and let A = xyT. (a) Show that {x} is a basis for the column space of A and that {yT} is a basis for the row space of A. (b) What is the...

prepare an alphabetical list of all Economics majors that entered the university in 2 0 2 1 the list should only display first and last names

What's the taxable equivalent yield on a municipal bond with a yield to maturity of 6.25 percent for an investor in the 25 percent marginal tax bracket? (Round your answer to 2 decimal places.)...

Foreign Cars List Price in K Sale Price in K Days to Sell Total 9445.6 8966.0 11252.0 Mean 47.2 44.8 56.3 Median 49.0 45.4 53.0 Range (Max-Min) 87.3 87.1 102.0 St.Dev 26.0993 26.0304 30.9969 Co.Eff....