MATM1544_lecture 29.pdf - The image part with relationship ID rId7 was not found in the file MATM1544 LECTURE 29 Matrix multiplication II T 27(0)51 401

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9/11/2015 1 The image part with relationship ID rId7 was not found in the file. T: +27(0)51 401 9111 | [email protected] | MATM1544 LECTURE 29 Matrix multiplication II September 11, 2015 T: 051 401 9111 [email protected] CONTENT Multiplication of matrices Properties of matrix multiplication Alternative notation Transpose of a matrix Zero matrix Identity matrix Examples Exercises
9/11/2015 2 WHEN MAY WE MULTIPLY TWO MATRICES? We can only multiply an ° × ± matrix with an ± × ² matrix if ³ × ± times ± × ´ = ³ × ´ Let µ = · ¸ ¹ ¸ º ¸ , » = ¼ · ¼ ¹ ¼ ½ , All vectors with ¾ components each. Then µ» = · ¸ ¼ · ¹ ¸ ¼ · º ¸ ¼ · WHEN MAY WE MULTIPLY We can only multiply an ° × ± matrix with an ± × ² matrix. ³ × ¾ times ¾ × ´ = ³ × ´ Let µ = · ¸ ¹ ¸ º ¸ , » = ¼ · ¼ ¹ ¼ ½ , All vectors with ¾ components each. Then µ» = · ¸ ¼ · · ¸ ¼ ¹ ¹ ¸ ¼ · ¹ ¸ ¼ ¹ º ¸ ¼ · º ¸ ¼ ¹
9/11/2015 3 WHEN MAY WE MULTIPLY We can only multiply an ° × ± matrix with an ± × ² matrix. ³ × ¾ times ¾ × ´ = ³ × ´ Let µ = · ¸ ¹ ¸ º ¸ , » = ¼ · ¼ ¹ ¼ ½ , All vectors with ¾ components each. Then µ» = · ¸ ¼ · · ¸ ¼ ¹ ¹ ¸ ¼ · ¹ ¸ ¼ ¹ º ¸ ¼ · º ¸ ¼ ¹ WHEN MAY WE MULTIPLY We can only multiply an ° × ± matrix with an ± × ² matrix.

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