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erastova [34]
3 years ago
5

Let S = {A, B, C, D} be some set of four elements of a vector space. Suppose that D = 2A + B + 3C and C = A − B. Is {A, B, D} li

nearly dependent? Explain.
Mathematics
1 answer:
Olin [163]3 years ago
4 0

Answer:

As explained

Step-by-step explanation:

given that D = 2A + B + 3C and S = {A, B, C, D}, C = A − B

for {A, B, D}  to be linearly dependent implies that A B and D will have values that not dependent on the sample space C.

if C = A -B is substituted in the original equation, the generated equation, 5A -2B will have values each as against C which is linearly independent.

Also, D will have values that are linearly dependent.

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X+3y = 2
nalin [4]

Answer:

The value of "x" is 5.

Step-by-step explanation:

In order to solve this system of equations, we first have to take the first equation and use it to represent "y" in terms of "x". We do that in the following way...

x + 3y = 2\\3y = 2 - x\\y = \frac{2}{3} - \frac{x}{3}

Now, we need to take the second equation and substitute "y" for the equivalent value in terms of "x". After doing this we will get the following equation, which we can solve to get the value of "x".

4x - 3y = 23\\4x-3(\frac{2}{3} - \frac{x}{3}) = 23\\4x - 2 + x = 23\\5x - 2= 23\\5x = 25\\x = 5

Therefore, the value of "x" is 5.

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