2.1 - Math 2940 Solutions, Fall 2011 Section 2.1 3)...

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

View Full Document Right Arrow Icon
Math 2940 Solutions, Fall 2011 Section 2 . 1 3 ) Certainly the planes are changed. The last two have different equations after the addition. The new matrix is 1 0 0 1 1 0 0 0 1 so the the first column has changed. Clearly the coefficient matrix has changed. The solutions are still the same, namely x = 2, y = 3 z = 4. 5 ) If ( x, y, z ) satisfies the first two equations, it automatically satisfies the third equation. To find solutions we solve the first two equations. Adding - 1 times the first to the second gives y = 1. Plugging back into the first gives x + z = 1. So the typical solution is ( t, 1 , 1 - t ) where t can be any number. just choose three different values for t . 9 ) (a) 1 2 4 - 2 3 1 4 1 2 2 2 3 = 1 · 2 + 2 · 2 + 4 · 3 - 2 · 2 + 3 · 2 + 1 · 3 - 4 · 2 + 1 · 2 + 2 · 3 = 18 5 0 (b) 2 1 0 0 1 2 1 0 0 1 2 1 0 0 1 2 1 1 1 2 = 2 · 1 + 1 · 1 + 0 · 1 + 0 · 2 1 · 1 + 2 · 1 + 1 · 1 + 0 · 2 0 · 1 + 1 · 1 + 2 · 1 + 1 · 2 0 · 1 + 0 · 1 + 1 · 1 + 2 · 2 = 3 4 5 5 12 ) The products are z y x , 0 0 0 , 3 3 6 . 13 )(a) A matrix with m rows and
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.

Page1 / 2

2.1 - Math 2940 Solutions, Fall 2011 Section 2.1 3)...

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