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a) Determine whether set S given below is a basis for ℝ 3 . If not, explain why.
S= {(1,0,0),(0,1,0),(0,0,0)}
b) Find the rank of matrix D given below.
D= [0 3 9 0]
[-2 -1 1 -1]
[0 -1 -3 1]
A car tows a trailer and is restricted to pull a mass of not more than 500kg, the mass of each canned fish is 440g and the mass of each empty box is 27g. There are 15 boxes each contains 36 canned fish, determine the total mass in kg of each box
1. Determine whether the lines given by the equations below are parallel, perpendicular, or neither. Also, find a rigorous algebraic solution for each problem.
a. {3y+4x=12 \brace -6y=8x+1}
b. {3y+x=12 \brace -y=8x+1}
c. {4x-7y=10 \brace 7x+4y=1}
2. A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, is given by h(t)=-4.9t^2+24t+8 . What is the height of the building? What is the maximum height reached by the ball? How long does it take to reach maximum height? Also, find a rigorous algebraic solution for the problem.
3. A farmer finds that if she plants 75 trees per acre, each tree will yield 20 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 3 bushels. How many trees should she plant per acre to maximize her harvest? Also, find a rigorous algebraic solution for the problem.
24 pairwise different positive integer numbers are written on the board. Their mean value is equal to 38. Let M be the smallest of these numbers. Find the largest possible value of M.
classify the following as an english noun or sentence, mathematical expression or sentence
a.) m+3m=5
b.) 6/7
c.) 2+3+1=7
d.) Iu - vI
e.) x^2 = a-1
1). Determine whether set S given below is a basis for ℝ 3 . If not, explain why.
S = {(1,0,0),(0,1,0),(0,0,0)}
2). Find the rank of matrix D given below.
D = [0 3 9 0]
[-2 -1 1 -1]
[0 -1 -3 1]
Find the eigenvalues and corresponding eigenvectors of matrix G given below.
G= [2 -3]
[4 -5]
The left and right page numbers of an open book are two consecutive integers whose sum is 265. Find these page numbers.
what is a function?
The first 1st,5th and 10th term of a linear sequence are geometric progression. If the 2nd and 8th term of the linear sequence is 30, find the non-zero common difference of the linear sequence
