math125-lecture 3.1

math125-lecture 3.1 - m x n number of columns number of...

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Unformatted text preview: m x n number of columns number of rows These are the "dimensions" of the matrix a 11 a 12 a 13 . . . a 1 n a 21 a 22 a 23 . . . a 2 n A = . . . . . . . . . . . . . . . a m 1 a m 2 a m 3 . . . a mn Notation: A m x n Sec 3.1 Saturday, February 06, 2010 11:15 PM Section3dot1 Page 1 m x n number of columns number of rows These are the "dimensions" of the matrix a 11 a 12 a 13 . . . a 1 n a 21 a 22 a 23 . . . a 2 n A = . . . . . . . . . . . . . . . a m 1 a m 2 a m 3 . . . a mn Notation: A m x n A is a 2 x 3 matrix a 12 = 0 , a 23 = 2 3.1.1 Saturday, February 06, 2010 11:15 PM Section3dot1 Page 2 m x n number of columns number of rows These are the "dimensions" of the matrix a 11 a 12 a 13 . . . a 1 n a 21 a 22 a 23 . . . a 2 n A = . . . . . . . . . . . . . . . a m 1 a m 2 a m 3 . . . a mn Notation: A m x n A is a 2 x 3 matrix a 12 = 0 , a 23 = 2 If A = [ a ij ] and B = [ b ij ] are both m x n matrices, then the matrix sum of A and B is a matrix A + B = [ c ij ] whose entries c ij are computed as: c ij = a ij + b ij for all 1 i m , 1 j n 3.1.2 Saturday, February 06, 2010 11:15 PM Section3dot1 Page 3 m x n number of columns number of rows These are the "dimensions" of the matrix a 11 a 12 a 13 . . . a 1 n a 21 a 22 a 23 . . . a 2 n A = . . . . . . . . . . . . . . . a m 1 a m 2 a m 3 . . . a mn Notation: A m x n A is a 2 x 3 matrix a 12 = 0 , a 23 = 2 If A = [ a ij ] and B = [ b ij ] are both m x n matrices, then the matrix sum of A and B is a matrix A + B = [ c ij ] whose entries c ij are computed as: c ij = a ij + b ij for all 1 i m , 1 j n 4 + 1 0 + 1 5 + 1 5 1 6 A + B = = -1 + 3 3 + 5 2 + 7 2 8 9 3.1.3 Saturday, February 06, 2010 11:15 PM Section3dot1 Page 4 m x n number of columns number of rows These are the "dimensions" of the matrix a 11 a 12 a 13 . . . a 1 n a 21 a 22 a 23 . . . a 2 n A = . . . . . . . . . . . . . . . a m 1 a m 2 a m 3 . . . a mn Notation: A m x n A is a 2 x 3 matrix a 12 = 0 , a 23 = 2 If A = [ a ij ] and B = [ b ij ] are both m x n matrices, then the matrix sum of A and B is a matrix A + B = [ c ij ] whose entries c ij are computed as: c ij = a ij + b ij for all 1 i m , 1 j n 4 + 1 0 + 1 5 + 1 5 1 6 A + B = = -1 + 3 3 + 5 2 + 7 2 8 9 4 0 5 2 -3 A + C = + = not defined! -1 3 2 0 1 A and C are not the same size 3.1.4 Saturday, February 06, 2010 11:15 PM Section3dot1 Page 5 Let k be a scalar (i.e. a real number) and A = [ a ij ] a matrix. Then the scalar multiplication of the matrix A by the scalar k is the matrix k A defined by: k A = [ k a ij ] 3.1.5 Monday, February 15, 2010 6:24 AM Section3dot1 Page 6 Let k be a scalar (i.e. a real number) and A = [ a ij ] a matrix. Then the scalar multiplication of the matrix A by the scalar k is the matrix k A defined by: k A = [ k a ij ] 1 1 1 - 2 x 1 - 2 x 1 - 2 x 1 -2 -2 -2- 2 = = 3 5 7 - 2 x 3 - 2 x 5 - 2 x 7 -6 -10 -14 3.1.6 Monday, February 15, 2010 6:24 AM Section3dot1 Page 7 Let k be a scalar (i.e. a real number) and A = [ a ij ] a matrix.a matrix....
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math125-lecture 3.1 - m x n number of columns number of...

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