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Andrei [34K]
4 years ago
7

Consider the two numerical expressions below. Which one is true and which one is false? (9 1/2) 4 = 81 (4 1/6) 3 = 16

Mathematics
2 answers:
melomori [17]4 years ago
7 0
Both of them are false
crimeas [40]4 years ago
4 0
Do you mean exponents? If so then

<span>(9^1/2)^4 
= 9^(1/2 *4)
= 9^4/2
= 9^2
= 81 ....This is true
---------------------------

</span><span>(4^1/6)^3 
</span>= 4^(1/6 *3)
=4^3/6
=4^1/2
= sqrt (4)
= 2 .......not equal 16 .....so it's false

so answer

(9^1/2)^4  = 81 is true
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Answer:

We have the equation

c_1\left[\begin{array}{c}0\\0\\0\\1\end{array}\right] +c_2\left[\begin{array}{c}0\\0\\3\\1\end{array}\right] +c_3\left[\begin{array}{c}0\\4\\3\\1\end{array}\right] +c_4\left[\begin{array}{c}8\\4\\3\\1\end{array}\right] =\left[\begin{array}{c}0\\0\\0\\0\end{array}\right]

Then, the augmented matrix of the system is

\left[\begin{array}{cccc}0&0&0&8\\0&0&4&4\\0&3&3&3\\1&1&1&1\end{array}\right]

We exchange rows 1 and 4 and rows 2 and 3 and obtain the matrix:

\left[\begin{array}{cccc}1&1&1&1\\0&3&3&3\\0&0&4&4\\0&0&0&8\end{array}\right]

This matrix is in echelon form. Then, now we apply backward substitution:

1.

8c_4=0\\c_4=0

2.

4c_3+4c_4=0\\4c_3+4*0=0\\c_3=0

3.

3c_2+3c_3+3c_4=0\\3c_2+3*0+3*0=0\\c_2=0

4.

c_1+c_2+c_3+c_4=0\\c_1+0+0+0=0\\c_1=0

Then the system has unique solution that is (c_1,c_2c_3,c_4)=(0,0,0,0) and this imply that the vectors v_1,v_2,v_3,v_4 are linear independent.

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3 years ago
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Answer:

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Question 3
BigorU [14]

Answer:

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