Answer:
c
Step-by-step explanation:
Answer:
7A
Step-by-step explanation:
9514 1404 393
Answer:
B, C
Step-by-step explanation:
Linearly dependent sets can be found using row-reduction techniques. If a row ends up zero, then the set is linearly dependent. Equivalently, the determinant of a 3×3 matrix can be computed. If it is zero, the set is dependent. The cross-product of two 3-D vectors can be computed. If it is zero, the vectors are dependent.
Any set of vectors that has more elements than each vector does must necessarily be dependent.
It is helpful to be able to use a calculator capable of performing these calculations (as opposed to doing it by hand). The first attachment shows the result of computing the reduced row-echelon form of the first set of 3 vectors. The set is found to be independent.
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The second set of vectors is clearly dependent, as the second vector is 5 times the first.
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The third set contains more vectors than there are elements to a vector. Hence at least one of them can be created using some combination of the others. This set is dependent.
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The cross-product of the fourth set is non-zero, so it is independent. The second attachment shows the result of a row-reduction tool on these vectors.
Answer:
-1
Step-by-step explanation:
See the attachment for the polynomial long division. The constant in the quotient is -1.
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Here, there is a remainder of -x. If there were no remainder the constant in the quotient is the ratio of the constant in the dividend to the constant in the divisor: -2/2 = -1.
That could be a first guess in a "guess and check" solution approach.
<em>Guess</em>: first term of binomial quotient is (2x^3)/x^2 = 2x; last term of binomial quotient is -2/2 = -1. So, the quotient is guessed to be (2x -1).
<em>Check</em>: (2x -1)(x^2 -x +2) = 2x^3 -3x^2 +5x -2
Subtracting this from the actual dividend gives a remainder of -x. This has a lower degree than the divisor, so no further adjustment of the quotient is required.
So if you have two triangles and you can transform one of them into the other ,the two triangles are congruent