Lecture 4 Printed Notes

Ii matrix multiplication if a and b are two given

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Unformatted text preview: ྏ5 4⎦ྏ D=A −B [d ij ] = [aij ] + [bij ] ⎡ྎ9 − 1⎤ྏ B = ⎢ྎ ⎥ྏ ⎣ྏ0 2 ⎦ྏ ⎡ྎ3 2 1⎤ྏ C = ⎢ྎ ⎥ྏ ⎣ྏ6 4 5⎦ྏ ⎡ྎ3 + 9 2 − 1⎤ྏ ⎡ྎ12 1⎤ྏ Then, A + B = ⎢ྎ ⎥ྏ = ⎢ྎ ⎥ྏ ⎣ྏ5 + 0 4 + 2⎦ྏ ⎣ྏ 5 6⎦ྏ A+C is not defined since A is a 2 × 2 and C is a 2 × 3 matrix! ii) Matrix Multiplication If A and B are two given matrices, then the product AB is only defined if the number of columns of A is equal to the number of rows of B, and the product matrix has the number of rows of A and the number of columns of B. For this reason, AB may not be equal to BA! C = AB ⎡ྎ (a11b11 + a12b21 + + a1m bm1 ) ⎢ྎ(a b + a b + + a b ) 22 21 2 m m1 = ⎢ྎ 21 11 ⎢ྎ ⎢ྎ ⎣ྏ(an1b11 + an 2b21 + + anmbm1 ) (a11b1r + a12b2 r + + a1mbmr ) ⎤ྏ (a21b1r +...
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