Math 3A Section 1.pdf - Math 3A Part 1 Matrix Operation...

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Math 3A Part 1: Matrix Operation 01-Organizing Data into Matrices Vocabulary: Matrix-A rectangular array of numbers or expressions. Elements-An item in a matrix. Key Content: *Write the number of rows first and columns second. *The first number in the subscript gives the element’s row position & the second number gives the column position. 02-Adding & Subtracting Matrices Vocabulary: Zero Matrix- O or Om × n is the matrix whose elements are all zeros. It is the additive identity matrix for the set of all m × n matrices. Equal Matrices- Are matrices with the same dimensions and equal corresponding elements. Matrix Addition- To add matrices A and B with the same dimensions, add corresponding elements. Matrix Subtraction- To subtract matrices A and B with the same dimensions, subtract corresponding elements. Key Content:*Corresponding elementsare matrix elements in the same position in each matrix. *Formula:A+B=[A B C]+[R S T]=[A+R B+S C+T] *The Commutative Property of Additionstates that the order in which you add two matrices does not matter.[A+B=B+A] *The Associative Property of Additionshows that the way in which matrices are grouped and added together does not matter.[(A+B)+C=A+(B+C)] *The Identity Property of Additionshows that if you add the zero matrix to any matrix, the result is that matrix.[There exists a m × n matrix O such that O + A = A + O = A]
*The Inverse Property of Additionshows that if you add the opposite of a matrix and the matrix itself, the result will be the zero matrix.[A + (−A) = O] *The opposite, oradditive inverse,of matrix A is −A. −A is the matrix with elements that are the opposites of the corresponding elements of A. *The concept of equal matrices can help you find unknown matrix elements; if the two matrices are equal, their corresponding elements are equal. 03- Scalar Multiplication Vocabulary: Scalar- A real number used to multiply a matrix. Scalar Multiplication- An operation that multiplies each element in a matrix by a real number. -Posttest: 93.33% 04- Matrix Multiplication Vocabulary: Product Multiplication- If matrix A is an m × n matrix and matrix B is an n × p matrix, then the product matrix AB is an m × p matrix.

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