Question: Fix a column Y 0 in Rn and let U = [A in Mnn | AY = 0}. Show that dim U = n(n

Fix a column Y ≠ 0 in Rn and let
U = [A in Mnn | AY = 0}.
Show that dim U = n(n - 1).

Step by Step Solution

★★★★★

3.38 Rating (173 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Fix a column y 0 in R n and define T M mn R m by TA Ay for all ... View full answer

blur-text-image
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)

Word file Icon

950-M-L-A-L-S (6567).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Let x and y be vectors in Rn and let Q be an n x n orthogonal matrix. Show that if z = Qx and w = Qy then the angle between z and w is equal to the angle between x and y.

Q:

Let x and y be linearly independent vectors in Rn and let S = Span(x, y). We can use x and y to define a matrix A by setting A = xyT + yxT (a) Show that A is symmetric. (b) Show that N(A) = S. (c)...

Q:

Let u be a unit vector in Rn and let H = I - 2uuT. Show that H is both orthogonal and symmetric and hence is its own inverse.

Q:

Exercise 1. (CS3.3) In lecture, we defined the dot product geometrically as follows: p(u, v) = |lul|2|/v//2 cos(0), where 0 is the angle between u, ve R". One can show that this definition of the dot...

Q:

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...

Q:

Math 636 Midterm Quiz \u001a\u0014 \u0015 \u001b x1 2 1. The geometric interpretation of the following set W = R | x1 + x2 = 2 is x2 (a) a point in R2 . (b) a line in R2 passing through the origin....

Q:

Math 636 Midterm Quiz \u001a\u0014 \u0015 \u001b x1 2 1. The geometric interpretation of the following set W = R | x1 + x2 = 2 is x2 (a) a point in R2 . (b) a line in R2 passing through the origin....

Q:

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:...

Q:

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:...

Q:

In C++ Project requires code to be executable. Base Code is included at the bottom for your convenience. Base Code for your convenience: You will write an nxn tic-tac-toe game/program that utilizes...

Q:

Find Vo in the circuit shown using nodal analysis. 1 2 1

Q:

Which of the following are TRUE about link state routing protocols? Select all that apply. Yantnz: Nodes exchange link costs with all nodes in the network Nodes share routing tables with all nodes...

Q:

What basis of accounting and measurement focus do enterprise funds use? Does this mean they report all assets and liabilities associated with the enterprise fund activities

Q:

CPA QUESTION Two individuals signed a contract that was intended to be their entire agreement. The parol evidence rule will prevent the admission of evidence offered to: a. Explain the meaning of an...

Q:

Prove or disprove: The outer product of X and Y equals the outer product of Y and X.

Q:

Let W be an n 1 matrix such that WT W = 1. The n n matrix H = In - 2WWT is called a Householder* matrix. (a) Show that H is symmetric. (b) Show that H-1 = HT.

Q:

A circulant of order n is the n à n matrix defined by C = circ (c1, c2,..., cn) The elements of each row of C are the same as those in the previous rows, but shifted one position to the right...

Q:

The prices of 7 toasters x (in dollars) and their corresponding lifespan y (in years) are given in the below. price 32.00 20.50 36.00 44.50 16.50 25.00 38.00 lifespan 8.50 5.20 10.00 12.00 5.50 9.40...

Q:

Lewis Securities Inc. has decided to acquire a new market data and quotation system for its Richmond home office. The system receives current market prices and other information from several online...

Q:

Content Write a summary of the key elements of a term sheet, as well as the stages of VC funding. Not all startups seek funding from outside investors. However, in the search for a scalable,...