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For Problems 1-7, determine whether the given set
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- Solve 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_forwardSolve the following two problems. You can use your calculator or MATLAB, but you will need to justify your argument and conclusions 1. Consider the vectors (2, 1,0, 2], [3, 1, 0, 1], [1, 1,0,-1] in R. Decide whether they are linearly independent.arrow_forwardFor each of the following lists of vectors in R3, determine whether the first vector can be expressed as a linear combination of the other two. (a) (-2,0,3) ,(1,3,0),(2,4,-1) (b) (1,2,-3) ,(-3,2,1) ,(2,-1,-1) (c) (3,4,1) ,(1,-2,1), (-2,-1,1) (d) (2,-1,0) , (1,2,-3), (1,-3,2) (e) (5,1,-5) , (1,-2,-3), (-2,3,-4) (f) (-2,2,2) ,(1,2,-1) ,(-3,-3,3)arrow_forward
- Please answer this NEATLY, COMPLETELY, and CORRECTLY for an UPVOTE. A thermometer with an initial reading of 10°C is brought outside where ambient temperature is 35°C. After two minutes, the thermometer reading was observed at 14.5°C. What is the thermometer reading after three minutes? g. What is the thermometer reading after three minutes?***Note!For your basis, here are the questions for letters a-c which have already been answered in this link (https://www.bartleby.com/questions-and-answers/please-answer-this-neatly-completely-and-correctly-for-an-upvote.-a-thermometer-with-an-initial-read/16d543cc-a0e7-48c7-9eb0-5a7ba15c9d71), and for letters d-f (https://www.bartleby.com/questions-and-answers/a-thermometer-with-an-initial-reading-of-10c-is-brought-outside-where-ambient-temperature-is-35c.-af/9640044f-c1b9-4ce7-9671-0b88629c8d44):a. What is the working equation for this problem?b. What is the temperature of the surroundings?c. What is the general solution for the given radioactive…arrow_forward#4 Need parts A-Garrow_forward1. Write the vector H- 16 as a linear combination of the vectors and Darrow_forward
- For each of the following lists of vectors in R³, determine whether or not the first vector can be expressed as a linear combination of the other two. (a) (-2, 0,3), (1, 3,0), (2, 4, -1) (b) (1,2,3), (-3, 2, 1), (2, -1, −1) (c) (3, 4, 1), (1, -2, 1), (−2, —1, 1)arrow_forwardExpress each of the following vectors in R² as linear combinations of the vectors [3] and [3] (a) (b) (c) (d) 7 13 H 5 5 12 22 = || = = + + + + + 5 r 3 rarrow_forwardEvaluate the following problem.arrow_forward
- #7 Need help with parts 1 and 2arrow_forwardIf k is a real number, then the vectors (1, k), (k, k+ 56) are linearly independent precisely when k # a, b, where a = , 6 = and a < b.arrow_forwardFor the following problems, you need to provide a clear and detailed solution. Work Problem1 1 (a) [. - | Determine if the vectors 0 and| 1 span R³. -2 3 (b;. -- ] Can these three vectors form a basis for R'.arrow_forward
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