MATH 0180 Midterm: MATH 180 Brown Exam Culiuc m180sov1
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Suppose that that value associated with each interior node in the gure below is equal to the average. 23 (a) write two linear equations that must be satis ed by a and b. (b) write this system of equations in augmented matrix form and row reduce it to solve for a and b. 2 for each of the following statements, indicate whether it is true or false. 3 determine whether the columns of are linearly independent. Suppose that t : r2 r2 is a linear transformation which maps (cid:20) 1 (cid:20) 3. Suppose that running for one hour burns 450 calories and costs (worth of wear-and-tear on your. 6 find a matrix equation of the form ax = b whose solution set is equal to. Any correct de nitions are acceptable. (b) show that if t : rn rm is a linear transformation which is both one-to-one and onto, then m = n.
