Linear Combinations and Matrix Multiplication

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Department
Mathematics
Course
MATH 2331
Professor
Rita Jimenez Rolland
Semester
Spring

Description
Linear Algebra Notes Matrix Multiplication February 6, 2014 Linear Combinations of Vectors x1 1+ x2 2= v3! v3is a linear combinativ1and v2 A vector b 2 R is a linear combination of v1v2;::vm~2 R IF there are constan1s2▯ ;▯ m2 R;▯ ~ such that b 1 1+ ▯2 2+ ::: +m m~ 0 1 . ▯ ▯ ▯ ▯ ▯ ▯ Example. 3x1+ x2= 7 @ 3 1 . 7A v = 3 v = 1 v = 7 x1+ 2x2= 4 . 1 1 2 2 3 4 1 2 . 4 x 1 1 x2 2= v3! ~v3as a linear combination: 0 1 0 1 0 1 0 1 . . . . @ 1 2 . 4A ! @1 2 . 4 A ! @ 1 2 . 4A ! @1 0 . 2A x1= 2 . . . . x2= 1 ▯ ▯ 1 ▯ ▯ ▯ ▯0 ▯5
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