Question: Let A be a nonsingular n n matrix, and suppose that A = L1D1U1 = L2D2U2, where L1 and L2 are lower triangular, D1

Let A be a nonsingular n × n matrix, and suppose that A = L1D1U1 = L2D2U2, where L1 and L2 are lower triangular, D1 and D2 are diagonal, U1 and U2 are upper triangular, and L1, L2, U1, U2 all have 1's along the diagonal. Show that L1 = L2, D1 = D2, and U1 = U2.

Step by Step Solution

★★★★★

3.41 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

If L 1 D 1 U 1 L 2 D 2 U 2 then D 2 1 L 2 1 L 1 D 1 U 2 U 1 ... 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)

949-M-L-A-E (874).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Let D be a nonsingular n Ã n diagonal matrix and let (a) Show that (b) Show that and dmin-min ldil dmax=max ld,il Isisn condi( D) = condoo (D) =-max dmax dmin cond2(D) =

Let A be a 3 3 matrix and suppose that a1 - 3a2 + 2a3 = 0 (the zero vector) Is A nonsingular? Explain.

Let U be an n n upper triangular matrix with nonzero diagonal entries. (a) Explain why U must be nonsingular. (b) Explain why U-1 must be upper triangular.

Math 104A Homework #4 Instructor: Lihui Chai 1. Write a code to compute a natural spline S(x) which interpolates a collection of given points (x0 , y0 ), (x1 , y1 ), ..., (xn , yn ) where x0

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...

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...

CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...

Suppose that A and B are symmetric matrices. a. Show that there always exists a non-singular matrix, M, such that MTAM and MTBM are diagonal. Hint: Let C be a non-singular matrix such that CAC I, and...

Please don't skip any step Thank you . Let B be a nonsingular matrix and let A = BT - B (a) Show that A does not admit and LU decomposition. (b) Let T be a nonsingular matrix such that T'A admits an...

Question -1 Consider the vector space of all 10x10 diagonal matrices. The dimension of this vector space is 20. select one: a. True b. False Question -2 If a vector space does not have a finite basis...

Your corporation is considering replacing older equipment. The old machine is fully depreciated and cost $41,434.00 seven years ago. The old equipment currently has no market value. The new equipment...

Find the zeros of f(x) = 3x5 - 20x3. Then, without using a graphing calculator, state the zeros of f(x - 3) and f(x + 8).

When you have finished your paragraph, get together in groups and read your individual paragraphs aloud to each other. Then discuss the successes and challenges of this activity. Consider the...

Compare and contrast mainstream and political economy approaches to the aggregate expenditure model and aggregate demand and supply model.

Let Pi(xi, yi, zi), i = 1, 2, 3, be three points in 3-space. Show that is the equation of a plane (see Section 5.2) through points Pi, i = 1,2,3. 21 2 2 22 1

Prove properties (a) through (h) for the cross product operation.

Verify that each of the cross products u x v in Exercise 1 is orthogonal to both u and v. In Exercise 1 (a) u = 2i + 3j + 4k, v = -i + 3j - k (b) u = i + k, v = 2i + 3j - k (b) u = i - j + 2k, v = 3i...

Smaltz Enterprises is currently involved in its annual review of the firm's cost of capital. Historically, the firm has relied on the CAPM to estimate its cost of equity capital. The firm estimates...

deals with possible negative effects of converting financial statements from foreign operations into domestic currency for consolidated reporting in the home country, Operating exposure Translation...

Katherine Kocher has determined the following information about her own financial situation. Her checking account is worth $590 and her savings account is worth $1,200. She owns her own home that has...