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123 The matrix A = 2 5 3 is the coefficient matrix for the system of equations given in question #2 108 To answer this question, please refer to the Equivalent Statements Theorem 5.1.5 after finding the determinant of A requested in the first part. (i). Give det(A) (technology encouraged): -1 (ii). How many solutions does the system Ax-b have? 1 (iii). What is the rank of matrix A? 3 (iv). Do the row vectors of A form a basis for R³? yes (v). Is λ = 0 an eigenvalue of A? yes (vi). What is the nullity of A? 0 (vii) How many solutions does the system Ax = 0 have? infinitely many

123 The matrix A = 2 5 3 is the coefficient matrix for the system of equations given in question #2 108 To answer this question, please refer to the Equivalent Statements Theorem 5.1.5 after finding the determinant of A requested in the first part. (i). Give det(A) (technology encouraged): -1 (ii). How many solutions does the system Ax-b have? 1 (iii). What is the rank of matrix A? 3 (iv). Do the row vectors of A form a basis for R³? yes (v). Is λ = 0 an eigenvalue of A? yes (vi). What is the nullity of A? 0 (vii) How many solutions does the system Ax = 0 have? infinitely many

Advanced Engineering Mathematics
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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123 The matrix A = 253 is the coefficient matrix for the system of equations given in question #2 108 To answer this question, please refer to the Equivalent Statements Theorem 5.1.5 after finding the determinant of A requested in the first part. (i). Give det(A) (technology encouraged): -1 (ii). How many solutions does the system Ax=b have? 1 (iii). What is the rank of matrix A? 3 (iv). Do the row vectors of A form a basis for R³? yes (v). Is A = 0 an eigenvalue of A? yes (vi). What is the nullity of A? 0 (vii) How many solutions does the system Ax = 0 have? infinitely many
Transcribed Image Text:123 The matrix A = 253 is the coefficient matrix for the system of equations given in question #2 108 To answer this question, please refer to the Equivalent Statements Theorem 5.1.5 after finding the determinant of A requested in the first part. (i). Give det(A) (technology encouraged): -1 (ii). How many solutions does the system Ax=b have? 1 (iii). What is the rank of matrix A? 3 (iv). Do the row vectors of A form a basis for R³? yes (v). Is A = 0 an eigenvalue of A? yes (vi). What is the nullity of A? 0 (vii) How many solutions does the system Ax = 0 have? infinitely many
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