Not necessarily.
and
may be linearly dependent, so that their span forms a subspace of
that does not contain every vector in
.
For example, we could have
and
. Any vector
of the form
, where
, is impossible to obtain as a linear combination of these
and
, since
unless
and
.
Answer :
<h3>
<u>
=1048576 ways </u>
a student can answer the questions on the test if the student answers every question.</h3>
Step-by-step explanation:
Given that a multiple-choice test contains 10 questions and there are 4 possible answers for each question.
∴ Answers=4 options for each question.
<h3>
To find how many ways a student can answer the given questions on the test if the student answers every question :</h3>
Solving this by product rule
Product rule :
<u>If one event can occur in m ways and a second event occur in n ways, the number of ways of two events can occur in sequence is then m.n</u>
From the given the event of choosing the answer of each question having 4 options is given by
The 1st event of picking the answer of the 1st question=4 ,
2nd event of picking the answer of the 2nd question=4 ,
3rd event of picking the answer of the 3rd question=4
,....,
10th event of picking the answer of the 10th question=4.
It can be written as by using the product rule
<h3>∴ there are 1048576 ways a student can answer the questions on the test if the student answers every question.</h3>
Answer:
1. {xx < 13} 3. {yy < 5} 5. {tt > -42} 7. {dd ≤ 4}
9. {kk ≥ -3} 11. {zz < -2} 13. {mm < 29}
15. {bb ≥ -16} 17. {zz > -2} 19. {bb ≤ 10}
21. {qq ≥ 2} 23. ⎧
⎨
⎩
ww ≥ - _7
3
⎫
⎬
⎭
Lesson 0-7
1. {(−15, 4), (−18, −8), (−16.5, −2),
Step-by-step explanation:
ZX + Zz = 180°, without the actual
measu