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2.Matrices-Review

# 2.Matrices-Review - Aij is the quantity A of the ith row...

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A ij is the quantity A of the i th row and j th column
Square Matrix – Any matrix with equal number of columns and rows Row Matrix – All elements are in a single row

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[ ] Υ੟ Υ੟ Υ੟ Φ੯ Τ੏ ΢ਯ ΢ਯ ΢ਯ Σਿ Ρਟ = 5 1 4 1 2 6 4 6 3 A [ ] Υ੟ Υ੟ Υ੟ Φ੯ Τ੏ ΢ਯ ΢ਯ ΢ਯ Σਿ Ρਟ = 6 0 0 0 2 0 0 0 3 B [ ] Υ੟ Υ੟ Υ੟ Φ੯ Τ੏ ΢ਯ ΢ਯ ΢ਯ Σਿ Ρਟ = 1 0 0 0 1 0 0 0 1 C
[ ] Υ੟ Υ੟ Υ੟ Φ੯ Τ੏ ΢ਯ ΢ਯ ΢ਯ Σਿ Ρਟ = 1 6 4 0 2 8 0 0 7 A [ ] Υ੟ Υ੟ Υ੟ Φ੯ Τ੏ ΢ਯ ΢ਯ ΢ਯ Σਿ Ρਟ = 2 0 0 5 4 0 3 1 2 B [ ] Υ੟ Υ੟ Υ੟ Φ੯ Τ੏ ΢ਯ ΢ਯ ΢ਯ Σਿ Ρਟ = 0 0 0 0 0 0 0 0 0 C

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Two matrices ( [A] and [B]) can be added or subtracted if the numbers of rows and columns are identical. Add or subtract the A ij quantity to or from the corresponding B ij quantity.

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Υ੟ Υ੟ Υ੟ Φ੯ Τ੏ ΢ਯ ΢ਯ ΢ਯ Σਿ Ρਟ 5 4 3 4 1 5 3 7 2

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[ ] [ ] [ ] [ ] [ ] [ ] Υ੟ Υ੟ Υ੟ Φ੯ Τ੏ ΢ਯ ΢ਯ ΢ਯ Σਿ Ρਟ = Υ੟ Υ੟ Υ੟ Φ੯ Τ੏ ΢ਯ ΢ਯ ΢ਯ Σਿ Ρਟ + + + + + + + + + + + + + + + + + + = = Υ੟ Υ੟ Υ੟ Φ੯ Τ੏ ΢ਯ ΢ਯ ΢ਯ Σਿ Ρਟ = Υ੟ Υ੟ Υ੟ Φ੯ Τ੏ ΢ਯ ΢ਯ ΢ਯ Σਿ Ρਟ = 1 6 3 38 10 22 14 11 7 ) 6 )( 1 ( ) 1 )( 3 ( ) 2 )( 1 ( ) 0 )( 1 ( ) 1 )( 3 ( ) 3 )( 1 ( ) 4 )( 1 ( ) 0 )( 3 ( ) 1 )( 1 ( ) 6 )( 5 ( ) 1 )( 4 ( ) 2 )( 2 ( ) 0 )( 5 ( ) 1 )( 4 ( ) 3 )( 2 ( ) 4 )( 5 ( ) 0 )( 4 ( ) 1 )( 2 ( ) 6 )( 1 ( ) 1 )( 2 ( ) 2 )( 3 ( ) 0 )( 1 ( ) 1 )( 2 ( ) 3 )( 3 ( ) 4 )( 1 ( ) 0 )( 2 ( ) 1 )( 3 ( * 6 0 4 1 1 0 2 3 1 1 3 1 5 4 2 1 2 3 ; C C B A B A

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[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] Υ੟ Φ੯ Τ੏ ΢ਯ Σਿ Ρਟ × + × × + × = Υ੟ Φ੯ Τ੏ ΢ਯ Σਿ Ρਟ × Υ੟ Φ੯ Τ੏ ΢ਯ Σਿ Ρਟ = × Υ੟ Υ੟ Υ੟ Φ੯ Τ੏ ΢ਯ ΢ਯ ΢ਯ Σਿ Ρਟ = Υ੟ Υ੟ Υ੟ Φ੯ Τ੏ ΢ਯ ΢ਯ ΢ਯ Σਿ Ρਟ = 21 22 11 21 21 12 11 11 21 11 22 21 12 11 1 7 6 5 3 2 3 0 1 3 2 2 4 5 6 B A B A B A B A B B A A A A B

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