{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lecture_2 - MA 265 LECTURE NOTES WEDNESDAY JANUARY 9 Two...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MA 265 LECTURE NOTES: WEDNESDAY, JANUARY 9 Two Variables General Remarks. In the previous lecture, we gave several examples of systems of m equations in n = 2 variables. More generally, say that we have a system of linear equations in the form a 11 x + a 12 y = b 1 a 21 x + a 22 y = b 2 As in the previous lecture, we can express these linear equations as lines: y =- a 11 a 12 x + b 1 a 12 y =- a 21 a 22 x + b 2 a 22 If these lines have different slopes, i.e.,- a 11 a 12 6 =- a 21 a 22 = ⇒ a 11 a 22- a 12 a 21 6 = 0 then we expect to find precisely one solution. That means the system is consistent. However, if the slopes are equal, i.e.,- a 11 a 12 =- a 21 a 22 = ⇒ a 11 a 22- a 12 a 21 = 0 then we have parallel lines. We must consider the intercepts in order to determine whether the lines are different (i.e., no solutions) or overlap (i.e., infinitely many solutions). Three Variables Example. We now consider the case where we have n = 3 variables. Consider the linear system x + 2 y + 3 z = 6 2 x- 3 y + 2 z = 14 3 x + y- z =- 2 This is a system of...
View Full Document

{[ snackBarMessage ]}

Page1 / 2

lecture_2 - MA 265 LECTURE NOTES WEDNESDAY JANUARY 9 Two...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online