Section 2 Notes

Section 2 Notes - MATH 294 Ex 1.2.11 Solve the system using...

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

View Full Document Right Arrow Icon
MATH 294 Ex 1.2.11: Solve the system using Gauss-Jordan elimination. x 1 +2 x 3 +4 x 4 = - 8 x 2 - 3 x 3 - x 4 = 6 3 x 1 +4 x 2 - 6 x 3 +8 x 4 = 0 - x 2 +3 x 3 +4 x 4 = - 12 the augmented matrix -----------------→ 1 0 2 4 . . . - 8 0 1 - 3 - 1 . . . 6 3 4 - 6 8 . . . 0 0 - 1 3 4 . . . - 12 -→ - 3 × (1 st eq ) 1 0 2 4 . . . - 8 0 1 - 3 - 1 . . . 6 0 4 - 12 - 4 . . . 24 0 - 1 3 4 . . . - 12 -→ - 4 × (2 nd eq ) +2 nd eq 1 0 2 4 . . . - 8 0 1 - 3 - 1 . . . 6 0 0 0 0 . . . 0 0 0 0 3 . . . - 6 - 4 × (m4 th eq ) +m4 th eq -→ ÷ 3 1 0 2 0 . . . 0 0 1 - 3 0 . . . 4 0 0 0 0 . . . 0 0 0 0 1 . . . - 2 We get reduced row-echelon form (rref) of the initial matrix. Now we can easily write down the solution. Let’s put x 3 = t where t R (any real number). Then the solution is ( x 1 , x 2 , x 3 , x 4 ) = ( - 2 t, 4 + 3 t, t, - 2), t R . Ex 1.2.25 Suppose matrix A is transformed into matrix B by a sequence of elementary row operations. Is there a sequence of elementary row operations that transforms B into A? Solution: The answer is Yes, there is. We always have a log file containing the sequence of all elementary row operations. In order to get the original matrix A one first needs to invert the order of all operations in the log file and then execute the inverse operations. If an operation
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/26/2007 for the course MATH 2940 taught by Professor Hui during the Fall '05 term at Cornell.

Page1 / 3

Section 2 Notes - MATH 294 Ex 1.2.11 Solve the system using...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online