# Lect6 - Chapter 1 Matrices and Systems of Equations...

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Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Invertible matrix & System of linear equation Recall: A system of linear equations a 11 x 1 + ··· + a 1 n x n = b 1 . . . a m 1 x 1 + + a mn x n = b m can be represented as A x = b where A is m × n .

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Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Invertible matrix & System of linear equation Recall: A system of linear equations a 11 x 1 + ··· + a 1 n x n = b 1 . . . a m 1 x 1 + + a mn x n = b m can be represented as A x = b where A is m × n . When m = n and A is nonsingular, the matrix equation can be solved easily.
Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Invertible matrix & System of linear equation Recall: A system of linear equations a 11 x 1 + ··· + a 1 n x n = b 1 . . . a m 1 x 1 + + a mn x n = b m can be represented as A x = b where A is m × n . When m = n and A is nonsingular, the matrix equation can be solved easily. A x = b

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Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Invertible matrix & System of linear equation Recall: A system of linear equations a 11 x 1 + ··· + a 1 n x n = b 1 . . . a m 1 x 1 + + a mn x n = b m can be represented as A x = b where A is m × n . When m = n and A is nonsingular, the matrix equation can be solved easily. A x = b A - 1 ( A x ) = A - 1 b
Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Invertible matrix & System of linear equation Recall: A system of linear equations a 11 x 1 + ··· + a 1 n x n = b 1 . . . a m 1 x 1 + + a mn x n = b m can be represented as A x = b where A is m × n . When m = n and A is nonsingular, the matrix equation can be solved easily. A x = b A - 1 ( A x ) = A - 1 b ( A - 1 A ) x = A - 1 b

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Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Invertible matrix & System of linear equation Recall: A system of linear equations a 11 x 1 + ··· + a 1 n x n = b 1 . . . a m 1 x 1 + + a mn x n = b m can be represented as A x = b where A is m × n . When m = n and A is nonsingular, the matrix equation can be solved easily. A x = b A - 1 ( A x ) = A - 1 b ( A - 1 A ) x = A - 1 b I x = A - 1 b
Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Invertible matrix & System of linear equation Recall: A system of linear equations a 11 x 1 + ··· + a 1 n x n = b 1 . . . a m 1 x 1 + + a mn x n = b m can be represented as A x = b where A is m × n . When m = n and A is nonsingular, the matrix equation can be solved easily. A x = b A - 1 ( A x ) = A - 1 b ( A - 1 A ) x = A - 1 b I x = A - 1 b x = A - 1 b

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Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Invertible matrix & System of linear equation Example . Given that 1 4 3 - 1 - 2 0 2 2 3 - 1 = 1 12 - 6 - 6 6 3 - 3 - 3 2 6 2 . Solve the following system x 1 + 4 x 2 + 3 x 3 = 12 - x 1 - 2 x 2 = 24 2 x 1 + 2 x 2 + 3 x 3 = 0
Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Invertible matrix & System of linear equation (Cont’d) a 11 x 1 + ··· + a 1 n x n = b 1 .

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Lect6 - Chapter 1 Matrices and Systems of Equations...

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