Determine whether the statements that follow are true or false, and justify your answer.
20:Vector is a linear combination of and .
It is true that Vector is a linear combination of and .
A vector is said to be a linear combination of other vectors if it can be written as in the linear combination of other vectors.
Let vector is a linear combination of and .
Then it will imply
Now equating the matrix we will get
On solving above equations, we will get
Hence, it is true that Vector is a linear combination of and
Kyle is getting some flowers for Olivia, his Valentine. Being of a precise analytical mind, he plans to spend exactly $24 on a bunch of exactly two dozen flowers. At the flower market they have lilies ($3 each), roses ($2 each), and daisies ($0.50 each). Kyle knows that Olivia loves lilies; what is he to do?
Consider some particles in the plane with position vectors and masses .
The position vector of the center of mass of this system is
Consider the triangular plate shown in the accompanying sketch. How must a total mass of be distributed among the three vertices of the plate so that the plate can be supported at the point ; that is, ? Assume that the mass of the plate itself is negligible.
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