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MATRICES. TM. Presented by : Thabo Mahlaela (601496).
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Introduction. The topic is about matrices and its application. It begins by discussing how 3D animations in movies are created using matrices. It then goes on to define a matrix as a rectangular arrangement of numbers in rows and columns, with immense importance being attached to it in physics, computer science, and economics among other fields due to its ability to solve complex problems efficiently..
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Definitions of matrices What is Matrices?. 1x3 2x 2 3x3 4 x 4.
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Matrix operations. Addition of Matrices Matrices can be added provided they have the same dimensions, with the operation performed element-wise. For an example we can only add matrices A=1x3 with B=1X3 or 2X2 with 2x2 same applies to 3x3 with 3x3 or 4x4 with 4x4. If one dimension if 3 x 3 and other one is 3 x 1 it cannot be added. We classified addition with common factors of operations. Example 1 on Additions 2x2.
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Matrix operations. Subtractions of Matrices The operations of the subtraction it’s similar concept to the addition but the corresponding element in the same position are subtracted instead of added. To subtract two matrices, the corresponding elements in the same position are subtracted together. The matrix subtraction are commutative and associative, just like scalar addition and subtraction. Please the reference examples below. Example 1 on Subtractions.
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Matrix operations. Matrix multiplication is performed by taking the scalar or dot product of the rows of the first matrix and the column of the second matrix. The resulting matrix has a dimensions based on the number of rows in the first matrix and the number of columns in the second matrix. For example, we can multiply 1x3 with 1x3, 2x2 with 2x2, 3x3 with 3x3 or 3x1 with 3x1 or 3x3 with 3x1, 4x4 with 4x4, and 3x3 with 3 X 1 or 4 x 4 with 4 x 1. For example, if you multiply 3x5=15 & 5x3=15. In matrices it applies different for e.g. Therefore, AB it's not equal to BA. The orders matters in matrices A= 1 x 3 B= 3 x 1 A.B= 1 X3 . 3 X1 B.A = 3 X1 . 3X1 THEREFORE, BA DOES NOT EXIST IN MATRICES AS DISPLAY WITH THE PRODUCT OF 3X5 IS NOT THE SAME WITH 5X3..
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Matrix operations. Matrix multiplication has many practical applications, such as transforming coordinates in computer of linear equations, and modelling complex relationship in economic and social sciences..
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Conclusion. Application of Matrices Matrices can be represented and analyse linear transformations, which are fundamental in the field like computer graphics, physics and engineering. Matrices are used to organise and manipulate large datasets, enabling advanced statistical analysis and machine learning techniques. Matrix methods are employed to solve complex optimization problem in areas such as operations research, economic and engineering design..