Review for Exam 1-4 and final

# Review for Exam 1-4 and final - Review for Exam 1 Math 2373...

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Review for Exam # 1 Math 2373 Try to show All Steps!! These questions are similar to your homework problems !! These are sample questions, you are responsible for all materials covered for this test. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Review topics for Exam #1 : Sec 1.1 & 1.2 Reduced Echelon form System equation solve it by Gauss –Jordan method: o Many solution o One solution o No solution Homogenous system of equation Row operation properties Augmented matrix Sec 1.3 Vectors: o Add/subtracting o Linear combination of vectors o Subspaces of R n Sec 1.5 Norm Magnitude Dot product of vectors Find angle between two vectors Distance: Unit vector at the direction of a given vector (normalizing) o Orthogonal vectors o Basic properties of vectors Sec 2.1 and Sec 2.2 add / sub / multiply matrix Identity matrix I n / diagonal matrix / zero matrix Exponent s of square matrix Matrix notation for system of linear equation Properties of matrix

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1 __ Check if following matrices are in reduced row echelon form: ⎡⎤ ⎢⎥ ⎣⎦ 103 2 a) 0 0 1 8 014 9 1004 b) 0 1 0 5 0019 10032 c) 0 2 0 6 1 10012 0 00 d ) 0 0 2-Use Gaussian Jordan method to find solution to following system of equations: x+y=0 y+2z=-3 3x 2y+z=3 123 363 6 243 36 2 1 0 xxx −− +− += =- = 1 0 3- solve following homogeneous system of equations. 124 1234 240 2432 xxxx + + = 4 Given 10 012 2 1 A = and B = and C = 34 103 13 a) Find A.B b) Find B.A
c) Find 2 3( ΙΑ )+C d) Find A-B e) Find 2A +3C 5 __ Given matrix A is 4X2, B is 2X6 and C is 3X4 a) Find Size of the product of C.A.B b) Find size of the product C.A.B 6 Simplify following matrix expression: A(A-B)B+B2AB-3A 2 7-Given two vectors u = (2,1,-1) and v = (3,4,2) a) -3u + 2v b) u.v c) magnitude of u d) Angle between u and v e) Norm of vector u f) Find a unit vector at direction of vector u. 8 __ Check whether following spaces are subspace of R 3 space or not. a) Space W with (a, a 2 ,c) b) Space V with (a, a+b, -a)

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Review for Exam # 2 Math 2373 Try to show All Steps!! These questions are similar to your homework problems !! These are sample questions, you are responsible for all materials covered for this test. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Review topics for Exam #2 : Sec 2.3 1 - Find transpose of a matrix 2 - Symmetric matrix -what it is and how write 3 - Know properties of transpose - look at homework 4 - Trace of a matrix and its properties 5 - Anti-symmetric matrices - homework problem. Define and know how to come up with one Sec 2.4 1 - Inverse of a square matrix and how to find it using Gauss-Jordan method. No more than 2x2 or 3x3.
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## This note was uploaded on 10/20/2009 for the course MATH 2373 taught by Professor Staff during the Fall '08 term at Collin College.

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Review for Exam 1-4 and final - Review for Exam 1 Math 2373...

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