MATH 0180 Midterm: MATH 180 Brown Exam Culiuc m180rev1
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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. Ntsb = a at2 =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. If it is false, give a counterex- ample demonstrating that it is false. F (a) given a matrix a, there is only one matrix in row echelon form which is row equivalent to a. F then there are necessarily in nitely many solutions to the corresponding system of equations. (800%99) nose . F (d) every linear map from r10 to r5 is surjective but not injective. the ) I (e) the transpose of a times b is equal to the transpose of b times the transpose of a.
