Answer:
One Solution
Step-by-step explanation:
The correct options for the linear combinations of the vectors are given by:
A, B, C, D, E and F.
<h3>What is a span between two vectors?</h3>
The span between two vectors is the set that contains all linear combinations between these two vectors.
Supposing we have two vectors u1 and u2, as is the case in this problem, the infinitely many linear combinations have the following format:
k1u1 + k2u2
In which k1 and k2 are real numbers.
With k1 = 4 and k2 = -7, we get that option A is correct.
For option B, the vector 0 will always be a part of the span, as it can be formed with constants 0, hence it is correct.
The dimension of the span is of 3, as the vectors have 3 elements, hence option C is correct.
The underlying vectors will always also be part of the span, as they can be formed with their constant 1 and the others at 0, hence options D and F are correct.
The size of the span of any vectors is of infinity, hence option E is correct while option G is not.
More can be learned about linear combinations at brainly.com/question/15885826
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Quadratic formula
factoring
graphing
completing the square
factoring by grouping
Rational Roots Theorem
synthetic division
Take a look at <span>5x^2 – 34x + 24 = 0. The last term could have been the result of these different possible muliplications: 1*24, 2*12, 3*8, 4*6. The leading term is 5, whose factors are 5 and 1. Thus, possible rational roots would be
4/5 (the 4 is a factor of 24 and the 5 is a factor of 5) and 6/1 (the 6 is a factor of 24 and the 1 is a factor of 5).
Using synth. div. to check whether 6 is actually a root:
___________________
6 / 5 -34 24
30 -24
------ --------------------------
5 -4 0
since the remainder is 0, we can safely call 6 a "root."
Note the remaining coefficients, 5 and -4:
They correspond to the factor 5x - 4. If we set this difference = to 0, and solve for x, we get x = 4/5 (which is correct).
The roots of </span><span>5x^2 – 34x + 24 = 0 are x = 4/5 and x= 6/1.</span>
