Can anyone help with these linear algebra problems? thank you.

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3 4. 5 1—1 2 .Let/—l=[0 1 _3 . Find a vector as in N (A) and verify that it is orthogonal to the rows of A. 1 2 . Find a unit vector SE that is orthogonal to both a1 and (1,2. —1 . Let a1 = I—IOI—l Sb [\3 || 1 —2 1 .Leta= —2 ,b= 4 ,c= 0 1 —2 —1 (a) Show that b is parallel to a; and c is perpendicular to a. (b) Find P, the projection matrix onto 3, the span of a. (c) Find projs (b) and projs(c). (a) Find the equation of the straight line which best ﬁts the following points (—2, 3), (—1, 2), (0,2), (1,1), and (2,1). 1 —2 —1 0 . Find P, the projection matrix on C(A). 1 2 (b) Let A = I—'I—ll—II—l . The pressure P is a linear function of temperature T. For T = 1, P = 3. For T = 2, P = 4 and for T = 3, P = 4.5. What is the best guess fro P when T = 4'?

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