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For Problems 1-7, determine whether the given set
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- 1. 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_forwardPlease 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_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_forward
- For 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#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_forwardEvaluate the following problem.arrow_forward#7 Need help with parts 1 and 2arrow_forward
- Express 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_forwardLet A = - - 3 [1] [2] and b = 3 9 b2 Show that the equation Ax = b does not have a solution for some choices of b, and describe the set of all b for which Ax=b does have a solution. How can it be shown that the equation Ax=b does not have a solution for some choices of b? A. Find a vector x for which Ax=b is the identity vector. B. Row reduce the augmented matrix [ A b] to demonstrate that A b has a pivot position in every row. C. Find a vector b for which the solution to Ax=b is the identity vector. D. Row reduce the matrix A to demonstrate that A does not have a pivot position in every row. E. Row reduce the matrix A to demonstrate that A has a pivot position in every row.arrow_forwardA = {1,3,5}, B = {2,3} %3D Check ALL of the following Cartesian products to which the following elements belong: (a) (1,2) ОА. В х А ОВ. В х В ОС. Ах В OD. A x A (b) (3, 1) ОА. А х А ОВ. В х В ОС. Ах В OD. В x Aarrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning