# Lect4 - Chapter 1 Matrices and Systems of Equations...

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Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Matrix Multiplication - 4 views 4 views of matrix multiplication

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Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Homework 6 Reading Leon (7th edition): p.33 - p.36, p.38 - 39 Leon (8th edition): p.30 - p.33, p.35 - 36 Homework 6 Leon (7th edition): Chapter 1 Section 3 Qn. 1 (e) (f), 2, 3, 7 (a), 8, 9. Leon (8th edition): Section 1.3 Exercises: Qn. 1 (e) (f), 2, 3, 7 (a), 8. Section 1.4 Exercise: Qn. 6.
Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Block Multiplication Let A = a 11 a 12 ··· a 1 n a 21 a 22 ··· a 2 n . . . . . . . . . . . . a m 1 a m 2 ··· a mn and x = x 1 x 2 . . . x n Denote a j = a ( :, j ) . A x = x 1 a 1 + x 2 a 2 + ··· + x n a n viewed as a combination of columns of A , more exactly, called the linear combination of a 1 , a 2 , ··· , a n .

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Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Block Multiplication(Cont’d) Let A = a 11 a 12 ··· a 1 n a 21 a 22 ··· a 2 n . . . . . . . . . . . . a m 1 a m 2 ··· a mn and y = ± y 1 y 2 ··· y m ² Then y A = y 1 a ( 1,: ) + y 2 a ( 2,: ) + ··· + y m a ( m ,: ) which is a combination of rows of A .
Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Example . Let A = 3 2 1 - 1 and x = x 1 x 2 , b = 1 2 . (i) Evaluate A x . (ii) For what x will satisfy A x = b ?

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Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Example . Let A = 3 2 1 - 1 and x = x 1 x 2 , b = 1 2 . (i) Evaluate A x . (ii) For what x will satisfy A x = b ? Observation A system of linear equations can be represented as a matrix equa- tion
Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Consider ( * ) a 11 x 1 + a 12 x 2 + ··· + a 1 n x n = b 1 a 21 x 1 + a 22 x 2 + ··· + a 2 n x n = b 2 . . .

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Lect4 - Chapter 1 Matrices and Systems of Equations...

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