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Math 51 Stanford Homework Solutions

Spring 2000 Math 51 pdf files

Number Due Date Assignment
1 April 6
  • Problem File 1, problems 1-10
  • Read MATLAB Notes I
  • MATLAB Problem File I, problems 1,2
2 April 13
  • Problem File 1, problems 11-19
  • Read MATLAB Notes II
  • MATLAB Problem File I, problems 3-8
3 April 25
  • Problem File I, problems 20-31
  • Read MATLAB Notes III
  • MATLAB Problem File I, problems 9-11
4 May 4
  • Problem File I, problems 32-35
  • MATLAB Problem File I, problem 12
  • Problem File II, problems 1-7
  • Read MATLAB Notes IV
  • MATLAB Problem File II, problems 1-3
5 May 11
  • Multivariable Calculus Section 3.2, problems 2,8,10,13,16,21,27
  • Multivariable Calculus Section 3.4, problems 2,8,9,17,18,20,28,41
  • Multivariable Calculus Section 3.5, problems 3,8,15,19
  • Problem File II, problem 8
6 May 23
  • Multivariable Calculus Section 3.6, problems 4,7,15,23,24,30
  • Multivariable Calculus Section 3.7, problems 2,3,4,13,18,21,24,29,35
  • Multivariable Calculus Section 13.5, problems 6,8,13,21,23,28
  • Multivariable Calculus Section 13.9, problems 4,5,16,19,20
7 not turned in
  • Problem File II, problems 9-13

6.1 The augmented matrix is 

1 0 1 0 1 2 3 4 1 2 1 2

5 13 5

Its reduced row echelon form is 

1 0 0 1 0 1 0 1 0 0 1 1

1 0 4

There is no inconsistency, and z is a free variable, so there exist infinitely many solu- tions.

6.2 The augmented matrix is

[

1 2 3 2 1 2

1 1

]

Its reduced row echelon form is

[

1 2 3 0 1 8/3

1 1/3

]

There is no inconsistency, and z is a free variable, so

there exist infinitely many solutions.

6.3 The augmented matrix is 

1 2 1 2 2 1 3 1 2 1 2 3

0 8 0 7

Its reduced row echelon form is 

1 0 0 0 1 0 0 0 1 0 0 0

0 0 0 1

Thus the final equation of the reduced system is 0 = 1, which means there are no solutions.

6.7 (a) After switching rows 1 and 2, the reduced row echelon form is 

1 4 0 0 11 1 0 0 0

0 0 0

Here z is a free variable and the solutions are (4z/11,−z/11, z).

3