1 1 2
Let u: 2,v= 3 andw=
-1 3 h
Justify each of the following problems.
(A) For what values of h is w in Spancfw_u, v?
(B) For what values of h is cfw_u, v, w linearly independent?
A) ~\ l l 2 mug->22 I 'l 4 Z - ~lRRa>R5 I 'l 2.
~ - 4
\ 5 l h- RHR
THE MECHANICAL UNIVERSE
Video 50. Particles and Waves
What common phenomenon caused physicists to rethink the structure of matter?
What determines the color at which any body will glow?
At what color do all bodies initially glow?
1. Consuder a system, 4x1 + 8x2 = k'
Choose h and k such that the system has
(A) no solution
(B) a unique solution
(C) many solutions
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t 8 K N 0-4M8 53*
-4K+%=o d -8+\<4=0
haz cl \<+8
b UWRVKE solutioh?
L7 Ci _4\r\*9$
Do the columns of A span R3?
A has 5 MM and l ColqmrS. Mammwm numbcy of PNotg :
A C0 unit \VE (swat m QUE! w. Calwms of 1" d0 0t gm 1R .
l -2 . ). a
2 O O LY 0 \
A has pwok MUUQj F0W~
: COMWW of I" 394 \R5
The following matrix P is the transition matrix for the Markov Chain describing the movement
of the robot.
Let v be the probabiliy vector in
, whose i-th entry gives the probability that the robot starts in
room i at the 0-th minut