2.1 - Math 2940 Solutions Fall 2011 Section 2.1 3 Certainly...

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 Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 2

2.1 - Math 2940 Solutions Fall 2011 Section 2.1 3 Certainly...

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