Solution. To check whether the vectors are linearly independent, we must answer the following question: if a linear combination of the vectors is the zero vector, is it necessarily true that all the coefficients are zeros?
Suppose that
x 1 ⃗v 1 + x 2 ⃗v 2 + x 3 ( ⃗v 1 + ⃗v 2 + ⃗v 3 ) = ⃗0
(a linear combination of the vectors is the zero vector). Is it necessarily true that x1 =x2 =x3 =0?
We have
x1⃗v1 + x2⃗v2 + x3(⃗v1 + ⃗v2 + ⃗v3) = x1⃗v1 + x2⃗v2 + x3⃗v1 + x3⃗v2 + x3⃗v3
=(x1 + x3)⃗v1 + (x2 + x3)⃗v2 + x3⃗v3 = ⃗0.
Since ⃗v1, ⃗v2, and ⃗v3 are linearly independent, we must have the coeffi-
cients of the linear combination equal to 0, that is, we must have
x1 + x3 = 0 x2 + x3 = 0 ,
x3 = 0
from which it follows that we must have x1 = x2 = x3 = 0. Hence the
vectors ⃗v1, ⃗v2, and ⃗v1 + ⃗v2 + ⃗v3 are linearly independent.
Answer. The vectors ⃗v1, ⃗v2, and ⃗v1 + ⃗v2 + ⃗v3 are linearly independent.
Answer:
Get him to the vet right now
Explanation: that's poison to dogs.
En serio, no sé si esto es real o no
Answer:
E. strengthen a claim by indicating that it applies even to exceptional cases
Explanation:
Answer E
Correct. In this sentence, the author makes the claim that melancholy can make one’s imagination “torpid” (sluggish), and that lack of appropriate occasions can prevent the mind from coming up with “sallies and excursions” (clever remarks). He strengthens the claim by extending it to the most exceptional cases when he indicates that it applies to any mind “however volatile,” that is, even to those that are normally the liveliest and most wide-ranging.
Answer:
A) 30 cm
B) 20 cm
Explanation:
For the perimeter of rectangle B, I just imagined there was a cut horizontally through the middle. The length would be 5, since its half, and the width would be the same (10) because folding it into a rectangle only changes its length.
I added it up : 5+5+10+10= 30 cm
Rectangle B is 30 cm
For the perimeter of square C, you folded it again to make the width decrease by 5cm , so all the sides were 5cm.
5+5+5+5=20 cm
Square C is 20 cm
