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USPshnik [31]
3 years ago
9

Suppose v1 , v2 , v3 ,v4 are vectors in R3.

Mathematics
1 answer:
mestny [16]3 years ago
5 0

Answer:

a. These four vectors are dependent because there are columns of 3 by 4 matrix with one free variable.

b. If one is a multiple of other

c. c1v1 + c20 = 0 has nontrivial solution.

Step-by-step explanation:

Any set of 4 or more vectors must be linearly dependent. The non trivial combination of vector may produce zero as the set is linearly dependent. The vector v1 and v2 will be dependent if one is the multiple of the other.

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4 years ago
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Bad White [126]
\bf \begin{cases}&#10;c=\textit{caramel corn}\\&#10;b=\textit{buttered microwave popcorn}\\&#10;p=\textit{lightly buttered popcorn}&#10;\end{cases}

so... he sold 400 items, that means, whatever those quantities of c,b,p are, they add up to 400, thus

c+b+p = 400

now, the "c" sold for $10
the "b" sold for $8
and the "p" sold for $7

so, the amount of revenue on the "c" is 10 * c, or 10c
the revenue on "b" is 8*b or 8b
and the revenue on "p" is 7*p or 7p

whatever those amounts are, they ended up in $3,272
thus
10c + 8b + 7p = 3,272

now, he sold more lightly buttered, or "p", than just buttered corn or "b"
he actually sold twice as much, so whatever "b" is, "p" is twice that much
or 
p = 2b

thus      \bf \begin{cases}&#10;c+b+\boxed{p}=400\\\\&#10;\boxed{p}=2b\qquad thus\\\\&#10;c+b+\boxed{2b}=400\qquad or\\\\&#10;c+3b=400\implies c=\underline{400-3b}\\&#10;--------------\\&#10;10c+8b+7p=3272\qquad or\\\\&#10;10(\underline{400-3b})+8b+7(\boxed{2b})=3272&#10;\end{cases}

solve for "b", to see how many buttered microwave popcorn Mike sold

how many lightly buttered?  well, p = 2b
how many caramel ones?   well  c = 400 - 3b
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3 years ago
A manager received an invoice for $86.30 for 30gal ice cream. how much did each gallon cost? a $3.49 b $3.15 c $4.26 d $2.88
Vinil7 [7]
86.3 / 30 = 2.876

Therfore the answer is D $2.88
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4 years ago
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