4.Use the procedure of Gaussian elimination to reduce the matrix:10 1011 1 00H1 00 1 1 into a reduced row echelon form in which the0 1 1 0 10 0 1 1 1leftmost nonzero entry is normalized to 1 and off diagonal elements are all reduced to 0? Find the row space, rank and nullity of thematrix?

(.) Given matrix is , A = 1010111010100110110100111 (.) If A is a m×n matrix then by the…

Answered: 4. 1 0 1 0 1 1 1 0 1 0 Use the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A X 2) Consider a matrix M = (6 %) in block form, where A and B are square matrices. Prove that 0 B det (M) = det (A) det (B). Suggestion: Induct on the number of rows of A. Use cofactor expansions down the first column. Each of the cofactors appearing is a block matrix with one fewer rows than A.
Solve the equation Ax = b by using the LU factorization given for A. Also solve Ax = b by ordinary row reduction. A = y = 4 - 7 - 4 3 12 - 5 X = 4 3 -9 = 1 -1 00 10 3 - 4 1 Let Ly = b and Ux=y. Solve for x and y. 4 -7 -4 0 -4 - 1 0 0 - 1 Row reduce the augmented matrix [A b] and use it to find x. The reduced echelon form of [A b] is yielding x = 4 - 15 61
None
Find the singular values of the matrix A - -3 6 6 1 -2 -2 Note: this is not asking for the full decomposition, just the singular values.
2. A nilpotent matrix is a square matrix A € Mnxn (F) such that Ak = 0, for some integer k. -3 1 0 2 3 -1 (b) Prove that every nilpotent matrix is not invertible. (a) Show that the matrix B = 1 2 - is nilpotent.
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Solve the given set of equations by applying L-U decomposition method. The upper triangular matrix U should include 1’s on its diagonal. -2.2a-5.72b-2.64c=-11.44 2.5a+4.1b+9.72c=1.576 -a-0.5b-5.68c=3.116
And obtain the values of ß¡ and B2. In matrix notation it can be shown that ß = (X'X)-'x'y a 01 i. What happens to ß when there is perfect collinearity among the X's? ii. How would you know if perfect collinearity exists? 02 Vou are given the following data:
We throw a symmetrical dice twice. Let X denote the number of throws in which an odd number of dice fell, and let Y denote the remainder of the product of the dice's rolls divided by 3.Check whether the variables X and Y are (a) independent (b) uncorrelated
q1
4. Let A be a nonzero 3 x 3 matrix such that A? = 0. (i) By showing the column space of A is contained in the null space of A, show that rank(A) < nullity (A). (ii) Using your answer from part (i), show that rank(A) = 1. %3D

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4. 1 0 1 0 1 1 1 0 1 0 Use the procedure of Gaussian elimination to reduce the matrix: 1 0 0 1 1 into a reduced row echelon form in which the 0 1 1 0 1 00111 leftmost nonzero entry is normalized to 1 and off diagonal elements are all reduced to 0? Find the row space, rank and nullity of the matrix?