Answer:
I.
A is a 4 x 5 matrix => A: U -> V, dim U = 5, dim V = 4
Null space is exactly two dimensional plane
dim null (A) = 2
II.
Rank A = dim U - dim Null A = 5 - 2 = 3
III.
Number of linearly Independent columns of A is the rank of A = 3
IV.
Yes, The system Ax = b has no solution sometimes as range of A \neq V
V.
Yes,Sometimes Ax = b has a unique solution
VI.
Yes, sometimes Ax = b has infinitely many solutions
So you know the whole line is XZ which is 83.Then you find out it is in two parts so that is XY and YZ which are 11 and 4c. You can make the equation:
11+4c=83
4c=72
c=18
c=18 and YZ=72
Direct variation is of the form y=kx. We are given the point (8, -4) so we can solve for k, the constant of variation...
-4=8k, divide both sides by 8
-4/8=k
k=-0.5, so our equation is:
y=-0.5x,
The probability that Boris will win the contest is:
P = 0.286
<h3>
How to get the probability?</h3>
For some given odds a:b, the probability is just computed as the quotient between a and b, which gives:
P = a/b
In this case, the odds are 2:7, so the probability that Boris will win the contest is:
P = 2/7 = 0.286
Written in percentage form, we get:
P = 28.6%
If you want to learn more about probability:
brainly.com/question/24756209
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