Biomech-Matrices Vectors Moments-Lecture

# Biomech-Matrices Vectors Moments-Lecture - Matrices,...

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Matrices, Vectors, and Moments Introduction to Biomaterials 14:125:208

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Matrices You can multiply two matrices if the number of columns in the first matrix equals the number of rows in the second matrix. If not, it is undefined The product matrix's dimensions are (rows of first matrix) × (columns of the second matrix )
Matrices

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Matrices Consider the following Similarly - - - = - - - = + + - - - + + - + + - - + + + - - + + - = - - - = - - = 4 5 4 2 4 1 0 3 0 1 0 7 1 1 0 0 2 2 1 0 2 1 1 2 2 1 4 1 0 0 1 2 0 2 2 0 1 0 1 1 2 1 2 2 2 1 1 2 0 1 1 1 1 2 1 1 2 1 2 0 1 2 1 BA AB B A
Matrices The transpose of a matrix consists of switching the rows and columns Thus if A=aij AT=aji A symmetric matrix Where A=AT

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Matrices A special symmetric matrix is the identity matrix It can also be shown that AI = A = IA
Matrices The Determinant 2x2 matrix The determinant of Is and is written as

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Matrices Examples Find the determinants
Matrices Determinant of a 3x3 matrix Can be applied to this course The determinant is and is written as

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Matrices Example By definition Where So the determinant is:
Matrices

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Matrices
So how can we use matrices in biomechanics? We can use them to solve systems of

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## This document was uploaded on 11/04/2011 for the course BIOCHEMIST 208 at Rutgers.

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Biomech-Matrices Vectors Moments-Lecture - Matrices,...

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