Question: Prove Theorem 4.2. [A proof by induction would be appropriate here.] In theorem 4.2 The determinant of a triangular matrix is the product of the

Prove Theorem 4.2. [A proof by induction would be appropriate here.]
In theorem 4.2
The determinant of a triangular matrix is the product of the entries on its main diagonal. Specifically, if A = [aij) is an n × n triangular matrix, then
det A = a11 a22 ··· ann

Step by Step Solution

★★★★★

3.48 Rating (168 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

If A is lower triangular then A T is upper triangular Since by Theorem 410 det A ... 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)

859-L-A-L-S (2519).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Prove that the determinant of any triangular matrix, upper or lower, is the product down its diagonal.

The trace of an n X n matrix A = [aij] is the sum of the entries on its main diagonal and is denoted by tr(A). That is, tr(A) = a11 + a22 + + ann If A and B are n n matrices, prove the following...

Triangular Determinants Show that the determinant of an upper triangular matrix is the product of its diagonal elements. The diagonal matrix is a special case. The statement for a lower triangular...

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:...

I need to see how 28 36 and 47 are done please. 35. (a) then so is A + B. 17. Prove Theorem 3.2(a)-(d). 18. Prove Theorem 3.2(e)-(h). (b) Prove that if A is a symmetric non matrix, the is KA for any...

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...

Course is linear algebra. I have attached the theorem as needed. Write a computer program to compute the QR factorization of a 5x5 matrix, either by 1. using rotators. Use the algorithm described in...

Write a computer program to compute the QR factorization of a 5x5 matrix, either by 1. using rotators. Use the algorithm described in the proof of Theorem 3.2.21; or 3. ysing reflectors Test your...

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

Q. 1 (1) The magnitude of the vector drawn in a direction perpendicular to the surface +2y + at the point (1,-1,2)is(a)2/3(b)3/2(c)3(d)6 CLO-1 (5) (2) If u =x* +y* +2* and r =x +yj+zk, then...

Roger Rong borrowed $12,000 on 120 - day 11 percent note. Roger paid $4,000 toward the note on day 40. On day 110 he paid an additional $3,000. Using the U.S. Rule his adjusted balance after the 1st...

For each of the following variables, determine whether the variable is categorical or numerical. If the variable is numerical, determine whether the variable is discrete or continuous. a. Number of...

Apply the ML procedure described in Section 7.2.3 and the EGLS estimator of Section 7.2.2 to estimate the cointegration relation and the other parameters of a VECM with cointegration rank r = 1, two...

Show that (A + ) + = A. [Show that A satisfies the Penrose conditions for A + . By Exercise 52, A must therefore be (A + ) + .]

Let and (a) Compute cond 1 (A). (b) Suppose A is changed to How large a relative change can this change produce in the solution to Ax = b? (c) Solve the systems using A and A' and determine the...

Let C be a linear (n, k, d) code with parity check matrix P. Prove that d = n - k + 1 if and only if every n - k columns of P are linearly independent.

To calculate the number of years until maturity, assume that it is currently May 2013. Required: In the above table, find the Treasury bond that matures in May 2024. What is the coupon rate for this...

(a) Wishland Sdn Bhd is seeking a loan for a period of one year for its intended purchase of three new machines. The cost of one machine is RM75,000 and 60 percent of financing is required. Wishland...

Hickock, Inc., is proposing a rights offering. Presently there are 600,000 shares outstanding at $47 each. There will be 120,000 new shares offered at $38 each. a. What is the new market value of the...