Elementary & Intermediate Algebra with Access Code
3rd Edition
ISBN: 9780321915139
Author: Michael III Sullivan
Publisher: PEARSON
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Chapter 2.2, Problem 57E
To determine
To solve: The linear equation
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Name
Assume there is the following simplified grade book:
Homework Labs | Final Exam | Project
Avery
95
98
90
100
Blake
90
96
Carlos
83
79
Dax
55
30
228
92
95
79
90
65
60
Assume that the weights used to compute the final grades are homework 0.3, labs 0.2,
the final 0.35, and the project 0.15.
| Write an explicit formula to compute Avery's final grade using a single
inner product.
Write an explicit formula to compute everyone's final grade simultane-
ously using a single matrix-vector product.
1. Explicitly compute by hand (with work shown) the following Frobenius inner
products
00
4.56 3.12
(a) ((º º º). (156
(b)
10.9
-1
0
2)),
Fro
5')) Fro
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- For the matrix A = = ( 6 }) . explicitly compute by hand (with work shown) the following. I2A, where I2 is the 2 × 2 identity matrix. A-1 solving the following linear systems by using A-¹: c+y= 1 y = 1 (d) (e) (f) A² find the diagonal entries of Aarrow_forwardIf 3x−y=12, what is the value of 8x / 2y A) 212B) 44C) 82D) The value cannot be determined from the information given.arrow_forwardC=59(F−32) The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true? A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 59 degree Celsius. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit. A temperature increase of 59 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius. A) I onlyB) II onlyC) III onlyD) I and II onlyarrow_forward
- (1) Let F be a field, show that the vector space F,NEZ* be a finite dimension. (2) Let P2(x) be the vector space of polynomial of degree equal or less than two and M={a+bx+cx²/a,b,cЄ R,a+b=c),show that whether Mis hyperspace or not. (3) Let A and B be a subset of a vector space such that ACB, show that whether: (a) if A is convex then B is convex or not. (b) if B is convex then A is convex or not. (4) Let R be a field of real numbers and X=R, X is a vector space over R show that by definition the norms/II.II, and II.112 on X are equivalent where Ilxll₁ = max(lx,l, i=1,2,...,n) and llxll₂=(x²). oper (5) Let Ⓡ be a field of real numbers, Ⓡis a normed space under usual operations and norm, let E=(2,5,8), find int(E), b(E) and D(E). (6) Write the definition of bounded linear function between two normed spaces and write with prove the relation between continuous and bounded linear function between two normed spaces.arrow_forwardind → 6 Q₁/(a) Let R be a field of real numbers and X-P(x)=(a+bx+cx²+dx/ a,b,c,dER},X is a vector space over R, show that is finite dimension. (b) Let be a bijective linear function from a finite dimension vector ✓ into a space Yand Sbe a basis for X, show that whether f(S) basis for or not. (c) Let be a vector space over a field F and A,B)affine subsets of X,show that whether aAn BB, aAU BB be affine subsets of X or not, a,ẞ EF. (12 Jal (answer only two) (6) Let M be a non-empty subset of a vector space X and tEX, show that M is a hyperspace of X iff t+M is a hyperplane of X and tЄt+M. (b) State Jahn-Banach theorem and write with prove an application of Hahn-arrow_forward(b) Let A and B be two subset of a linear space X such that ACB, show that whether if A is affine set then B affine or need not and if B affine set then A affine set or need not. Qz/antonly be a-Show that every hyperspace of a vecor space X is hyperplane but the convers need not to be true. b- Let M be a finite dimension subspace of a Banach space X show that M is closed set. c-Show that every two norms on finite dimension vector space are equivant (1) Q/answer only two a-Write the definition of bounded set in: a normed space and write with prove an equivalent statement to a definition. b- Let f be a function from a normed space X into a normed space Y, show that f continuous iff f is bounded. c-Show that every finite dimension normed space is a Banach. Q/a- Let A and B two open sets in a normed space X, show that by definition AnB and AUB are open sets. (1 nood truearrow_forward
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