Algebra question and answers for July 23, 2023
- Q Let A be a 6 x 6 matrix with characteristic polynomial det (?I - A) = ?(?+3)(?-2).Which of the following statements are True? Select ALL that apply.The matrix ? is...
- Q ?4. Let L: R5 R be a linear transformation, and let S = (v?, 2, 3} be an indexed subset ofR. Suppose that {L(v?), L(v?), L(vs)} is linearly independent. Show...
- Q (3 points) Let S = {?, 2, 2 be a subset of an inner product space V. Show that if Sorthonormal set, then S is linearly independent.
- Q Let S = {v1, v2, v3} be a subset of an inner product space V. Show that if S orthonormal set, then S is linearly independent.
- Q 2. Solve each of the following initial value problems:(a) y=-y?+ 2y?y/? = 2y? - y?y?(0) = 3, y?(0) = 1(b) y yi-2y2=y? = 2y? + y?y?(0) = 1, y2(0)=-2(c) y...
- Q 1. (5 points) Let P3 be the vector space of all polynomials of degree less than 4, with anorthonormal basis {f1, f2, f3, fa}. Let f P3 be such that(f.f?)=Given...
- Q Several customers order small fruit baskets filled with apples, bananas, and oranges. Let a represent the price perpound of apples, b represent the price per pound of bananas, and c...
- Q Which system is independent and inconsistent?[x-y+z=2O x-y-z = 2x+y+z=2x-y+z=2Ox+y-z=3|x-y-z=4OO[2x+2y+2z=4-x-y-z=-2x+y+z=2x-y-z=2x+y-z=3|-x+y+z=4Mtal
- Q Given a planar graph G such that all the vertices have even degrees: Prove that all theregions separated out by this graph (all the faces) can be 2-colored. That is,...
- Q Question 8. Given internal angle A = 30 and side b= 10in. What side length a results ina unique triangle ABC?
- Q The manufacturer of a wine bottle spends $5.20 to make each bottle and sells them for $10.40. The manufacturer also has fixed costs each month of $5000.Find the cost function,...
- Q Define T: P? P? byT(ag + a?x + a?x) = (-3a? + 5a?) + (-4a0 +4a?-10a2)x+ 5a?x.Find the eigenvalues. (Enter your answers from smallest to largest.)(A1, A2, A3)-2,4,6Find the corresponding...
- Q Write the number in standard notation, without exponents.7.4x10^7
- Q Find a basis for the orthogonal complement of the subspace of R4 spanned by the vectors.V? = (1, 5, -4,4), v?=(2, 9, 0, 2), v3 = (1,4,4,-2)The basis for the...
- Q Let f(x) = 3x - 1 and g(x) = x - 4.Find (fog)(1).
- Q Identify the coordinate space to which P6 is isomorphic.
- Q Determine two vectors that are perpendicular to each other and also perpendicular to u= [2, 7, -1]. It is also known, that one of these vectors, creates two equal angles...
- Q Sean, Angelina, and Sharon went to an office supply store. Sean bought 7 pencils, 8 markers, and 7 erasers, His total was $22.00. Angelina spent $19.50 buying 4 pencils, 8...
- Q Use Gaussian elimination to find the values of a for which the equation systemx + y = 2z = a +73x - y + az = -3-x + ay -...
- Q Find the amount of time required for a $ 21,000 investment to double if the annual interest rate r is 9.2% and interest is compounded continuously. Round your answer to...
- Q Find the determinant of the following matrix using the co-factor expansion method.A= 1 -1 2 -2 2 -3 1 1...
- Q When using elimination and substitution, ex-plain how to recognize a system of linearequations that has no solutions.When using elimination and substitution, ex-plain how to recognize a system of linearequations that...
- Q The cost for three packages of moving boxes is modeled by the system of equations below. Let s represents the costof each small box, m represents the cost of each...
- Q 1 -12 -3)Given the following matrices A =3B = (-1).2[i] Calculate 2A - B.[ii] Find AT[iii] Calculate AB.[iv] Based on your results from part [iii], what can youconclude about the...
- Q Find a basis for the solution space for AX = 0 where AWhat is the dimension for this solution space?
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