# Prelim1_sol - Solution for prelim 1 Math 294 spring 2005 1a This is a hw problem see hw solution for problem(17 in section 2.2 1b Since A is a

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Solution for prelim 1 Math 294 spring, 2005 1a. This is a hw problem, see hw solution for problem (17) in section 2.2. 1b. Since A is a reflection, the inverse of A is itself, that is, 1 AA = (Recall HW problem 41 in section 2.3). 2a. This is also a hw problem, see hw solution for problem (19) in section 2.3. 2b. It is not invertible. To see this, note that if A is invertible if and only if the RREF A is the identity matrix. However, if two columns of A are identical, then, the RREF A cannot be the identity matrix since the two columns of A that are identical will be transformed, after row reduction, to two columns that are identical. (Recall that the columns of an identity matrix are all different). 3 Let 1 2 3 4 x x x x x   =  G be any vector that is perpendicular to 12 11 02 , 13 04 vv   ==  GG . The conditions 0 xv xv •=•= GG GG is equivalent to the linear systems 1234 0 2340 xx xxxx + = + ++ = The homogeneous solution of this system is, using row operations, 10100 12340 02240 01120 A

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## This note was uploaded on 04/04/2008 for the course MATH 2940 taught by Professor Hui during the Spring '05 term at Cornell University (Engineering School).

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Prelim1_sol - Solution for prelim 1 Math 294 spring 2005 1a This is a hw problem see hw solution for problem(17 in section 2.2 1b Since A is a

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