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?
Kyle would buy bouquet of consisting of lilies, roses and daisies.
Let ‘l’ represents the number of lilies, ‘r’ represents the number of roses and ‘d’ represents the number of daisies.
The sum of number of flowers should be equal to .
The equations are,
Perform the operation on equations,
Perform the operation on equations, .
Choose the value of ‘d’ such that the values of ‘l’ and ‘r’ are positive.
Using trial and error method, the value should be,
Substitute this value in the equations (3) and (4)
The number of lilies, roses and daisies are, .
Hence, Kyle would buy a bouquet of consisting of lilies, roses and daisies.
If you sell two cows and five sheep and you buy pigs, you gain coins. If you sell three cows and three pigs and buy nine sheep, you break even. If you sell six sheep and eight pigs and you buy five cows, you lose coins. What is the price of a cow, a sheep, and a pig, respectively? (Nine Chapters, Chapter 8, Problem 8)
Recall that a real square matrix A is called skew symmetric if .
a. If A is skew symmetric, is skew symmetric as well? Or is symmetric?
b. If is skew symmetric, what can you say about the definiteness of ? What about the eigenvalues of ?
c. What can you say about the complex eigenvalues of a skew-symmetric matrix? Which skew-symmetric matrices are diagonalizable over ?
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