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MATH-M 344 Chapter 7: M344 7.3 Notes (Jan. 25)

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16 Feb 2017

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M344 section 7. 3 notes- systems of linear algebraic equations; linear independence; eigenvalues and. System of linear equations has form {(cid:1853)(cid:2869)(cid:2869)(cid:2869)+(cid:1853)(cid:2869)(cid:2870)(cid:2870)+(cid:1710)+(cid:1853)(cid:2869)=(cid:1854)(cid:2869) (cid:1853)(cid:2870)(cid:2869)(cid:2869)+(cid:1853)(cid:2870)(cid:2870)(cid:2870)+(cid:1710)+(cid:1853)(cid:2870)=(cid:1854)(cid:2870) (cid:1709) (cid:1853)(cid:2869)(cid:2869)+(cid:1853)(cid:2870)(cid:2870)+(cid:1710)+(cid:1853)=(cid:1854: let =[(cid:1853)(cid:3036)(cid:3037)] be (cid:1866) (cid:1866) matrix, let (cid:2184)=(cid:4666)(cid:1854)(cid:2869),(cid:1854)(cid:2870), ,(cid:1854)(cid:4667) be vector (equivalent to (cid:1866) (cid:883) matrix) in , want to find (cid:1866) (cid:883) matrix/(cid:1866)-vector such that =(cid:2184) If invertible, system =(cid:2184) has unique solution = (cid:2869)(cid:2184) (cid:883) (cid:883)], (cid:2184)=[(cid:883)(cid:884)] (cid:884: =[(cid:883, det=(cid:883)(cid:4666) (cid:883)(cid:4667) (cid:4666) (cid:883)(cid:4667)(cid:4666)(cid:884)(cid:4667)=(cid:883) (cid:882) invertible, (cid:2869)=(cid:2869)(cid:2869)[ (cid:883) (cid:884) (cid:883)] (cid:883) Solve the system {(cid:2869)+(cid:2870)=(cid:883) (cid:884)(cid:2869)+(cid:884)(cid:2870)=(cid:884) : =[(cid:883) (cid:883)(cid:884) (cid:884)], (cid:2184)=[(cid:883)(cid:884), det=(cid:883)(cid:4666)(cid:884)(cid:4667) (cid:884)(cid:4666)(cid:883)(cid:4667)=(cid:882) not invertible. Has 1 free variable ((cid:2870))- second column does not have pivot (leading nonzero) entry. (cid:2869)=(cid:883) (cid:2870) (write pivot variable in terms of free variable) Infinitely many solution vectors possible; (cid:2870) is an arbitrary parameter that can be any scalar: set of vectors {(cid:2778),(cid:2779), ,(cid:2193)} is linearly independent if the only set of constants {(cid:1855)(cid:2869),(cid:1855)(cid:2870), ,(cid:1855)(cid:3038)} that satisfies (cid:1855)(cid:2869)(cid:2778)+(cid:1855)(cid:2870)(cid:2779)+(cid:1710)+(cid:1855)(cid:3038)(cid:2193)=(cid:2777) is (cid:1855)(cid:2869)=(cid:1855)(cid:2870)=(cid:1710)=(cid:1855)(cid:3038)=(cid:882) No dependence relation between the (cid:2191) can be obtained.

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S A carnival merry-go-round rotatexWeBWork: CSU MTH284 Fall18 x+ C Not secure webworks2.csuohio.e U MTH284 Fall18/HW4 EigenValues, Rod/17/user-2699769&effectiveUser-2699769&key-vYsrs1KsSmrZ4iwgsvaFAE 1PYWi..C Homework Sets HW4 EigenValues Rod: Problem 17 Prev Up Next (1 pt) Find a 2 Ã 2 matrix A for which HW4 EigenValues Rod Problem 17 Password/Email Grades .5 E-spanand E span Problems Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 where Ex is the eigenspace associated with the eigenvalueA .4 Note: You can eam partial credit on this probvem. Preview Answers Submit Answers You have attempted this problem 2 times. Your overall recorded score is 0% You have unlimited attempts remaining. Email instructor Activate Windows Go to Settings to activate Windows 10:58 PMM 12/1/20 ^
S A carnival merry-go-round rotatexWeBWork: CSU MTH284 Fall18 x+ C O Not secure webworks2.csuohio.e U MTH284_Fall18/HW4 EigenValues_Rod/18/ Homework Sets HW4 EigenValues Rod: Problem 18 Prev Up Next HW4 EigenValues Rod Problem 18 Password/Email Entered Answer Preview Result incorrect Grades Problems ncorrect Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 incorrect At least one of the answers above is NOT correct (1 pt) Find a 2 x 2 matrix A such that and -5 -3 are eigenvectors of A, with eigenvalues 5 and-10 respectively. Activate Windows Go to Settings to activate Windows Note: You can eam partial credit on this probvem. 10:58 PMM 12/1/20 ^
A carnival merry-go-round rotat D WeBWorK : CSU-MTH284-Fall18 x Ã Ð¡ Not secure I webworks2.csuohio.edu/webwork2/CSU-MTH284-Fall 18/HW4-EigenValue r-2699769&effectivelser=2699769&key=vYsrs1KsSmrZ4iwgsvaFAE 1PYWli â Logged in as 2699769 Log Out MATHEMATICAL ASSOCIATION OF AMERICA MAIN MENU Courses Homework Sets webwork/csu mth284 fall18I hw4_e eigenvaluesrod 20 HW4 EigenValues Rod: Problem 20 Prev Up Next (1 pt) HW4 EigenValues Rod Problem 20 Password/Email Grades 13 10 Problems Let M 5 -2 Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Find formulas for the entries of M, where n is a positive integer An-(n-1) Mn = Note: You can eam partial credit on this problem. Preview Answers Submit Answers You have attempted this problem 1 time. Your overall recorded score is 0% You have unlimited attempts remaining. Activate Windows Go to Settings to activate Windows Email instructor CSU MTH284 Fall13/HW4 EigenValues Rod21. 10:58 PMM 12/1/20 ^
A carnival merry-go-round rotat D WeBWorK : CSU-MTH284-Fall18 x C Not secure webworks2.csuohio.e U MTH284_Fall18/HW4 EigenValues_Rod/21/ Homework Sets HW4 EigenValues Rod: Problem 21 Prev Up Next HW4 EigenValues Rod Problem 21 Password/Email Entered AC Answer Preview Grades AC Problems Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 The answer above is NOT correct (1 pt) Which of the following transformations are linear? A. D.10 Ð£Ð· 2x1 Activate Windows Go to Settings to activate Windows Preview Answers Submit Answers Your score was recorded. You have attempted this problem 2 times 10:59 PMM 12/1/20 ^
S A carnival merry-go-round rotatexWeBWork: CSU MTH284 Fall18 x+ C Not secure webworks2.csuohio.e U MTH284_Fall18/HW4 EigenValues_Rod/23/ Homework Sets HW4 EigenValues Rod: Problem 23 Prev Up Next HW4 EigenValues Rod Problem 23 Password/Email Entered Answer Preview Result Grades incorret Problems incorrect Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 At least one of the answers above is NOT correct 3-6 21is a basis for IR (1 pt) The set B Find the coordinates of the vector relative to the basis B Note: You can eam partial credit on this probvem. Preview Answers Submit Answers Your score was recorded You have attempted this problem 3 times. You received a score of 0% for this attempt. Your overall recorded score is 0%. You have unlimited attempts remaining Activate Windows Go to Settings to activate Windows Email instructor 10:59 PMM 12/1/20 ^
A carnival merry-go-round rotat D WeBWorK : CSU-MTH284-Fall18 x C Not secure webworks2.csuohio.e U MTH284 Fall18/HW4 EigenValues, Rod/24/user-2699769&effectiveUser-2699769&key-vYsrs1KsSmrZ4iwgsvaFAE 1PYWi..C Homework Sets HW4 EigenValues Rod: Problem 24 Prev Up Next HW4 EigenValues Rod Problem 24 Password/Email Grades (1 pt) The vectors -2 -3 Problems Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 form a basis for R3 if and only if k38/11 Preview Answers Submit Answers You have attempted this problem 2 times. Your overall recorded score is 0% You have unlimited attempts remaining. Email instructor Activate Windows Go to Settings to activate Windows 10:59 PMM 12/1/20 ^