Consider the following linear system: -1, x2 + 2x3 + x4 -x1+ x2 – x3 – 2x4 2x1 + x2 + 8x3+7x4 -4x1 + 3x2 – 6x3 – 9x4 -3, 3, -11, in variables x1, X2, X3, and x4. Hint: You only have to row reduce one augmented matrix to answer all of the questions below. A. What is the reduced row echelon form of the augmented matrix? B. What is the rank of the matrix? C. Of the variables x1, x2, x3, and x4, which are free (i.e. independent) and whic are dependent? D. Write the general solution in parametric form. E. Let A be the coefficient matrix of the system. Is A invertible? F. What is the determinant of A? G. What is Nul(A)? H. Express Nul(A) in the form Span({ã1,...,ã}).
Consider the following linear system: -1, x2 + 2x3 + x4 -x1+ x2 – x3 – 2x4 2x1 + x2 + 8x3+7x4 -4x1 + 3x2 – 6x3 – 9x4 -3, 3, -11, in variables x1, X2, X3, and x4. Hint: You only have to row reduce one augmented matrix to answer all of the questions below. A. What is the reduced row echelon form of the augmented matrix? B. What is the rank of the matrix? C. Of the variables x1, x2, x3, and x4, which are free (i.e. independent) and whic are dependent? D. Write the general solution in parametric form. E. Let A be the coefficient matrix of the system. Is A invertible? F. What is the determinant of A? G. What is Nul(A)? H. Express Nul(A) in the form Span({ã1,...,ã}).
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter6: Matrices And Determinants
Section: Chapter Questions
Problem 4CC
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