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- Please explain and do all steps so that I can understand this question.arrow_forwardPlease solvearrow_forwardSolve the following exercises, you will need to show all your work to receive full credit. Consider the matrix, 2 1 -2 2 3 -4 1 1 1 - Knowing that f(t) = (t – 1)²(t - 2) is the characteristic polynomial, do the following: 1. find a basis of eigenvectors; 2. Find P such that P- AP is a diagonal matrix D. Give Darrow_forward
- Suppose the polynomial ax² + bx + c corresponds to the vector (a, b, c). 2 To what polynomial will (3,4,2) correspond? 3x+4x+2 2 To what polynomial will (3, -3, -5) correspond? 3x²-3x-5 To what polynomial should (3, 4, 2) + (3, -3, -5) correspond? 6x+x-3 What should the corresponding vector be? (6,1,-3) vector components) 2 To what polynomial should 2(3,4,2) correspond? 6x²+8x+4 J What should the corresponding vector be? (6,8,4) Submit Question A Part 2 of 5 Part 3 of 5 (Use to enclose the ▼ Part 4 of 5 Part 5 of 5 Based on the preceding, is there any significance to the componentwise sum of two vectors?" Defend your conclusion..arrow_forwardThank you for any help!arrow_forward1. Find all solutions: 2. In what ways can 88-8 and be written x+y ==0 a as a linear combination of [] [] [4], and ² 3. Show that the vector 2 is NOT contained in the span of the following three vectors 6 4. For which b are the vectors -0.0 x+2y+z=5 2x+3y-z=3 independent?arrow_forward
- Given the following vectors A=-4a+3a - 2a X y B=a +5a +7a_ y C=-2a-4a +6a X y 2 Evaluate |AX (BXC)|arrow_forwardFf.275.arrow_forwardAre the vectors 16 + 16x – 12x², – 12 – 12x – 12x? and 18 + 18x – 3x2 linearly independent? linearly independent If the vectors are independent, enter zero in every answer blank since zeros are only the values that make the equation below true. If they are dependent, find numbers, not all zero, that make the equation below true. You should be able to explain and justify your answer. 0 = (16 + 16x – 12x²)+ (-12 – 12x – 12x²)+ (18 + 18x – 3x?).arrow_forward
- 1. For the system below, describe the solutions in parametric vector form: + 3x3 + 2x2 + 5x3 2x1 + 3x2 + 8x3 X1 + X2 4 X1 7 || 11arrow_forwardA direction vector for a line is any vector that joins two points on that line. Find a 8. It is not certain that you and your classmates will get direction vector for 2x + 5y exactly the same answer. How should your answers be related, however?arrow_forwardPlease only do highlighted problemsarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage