TAMU Final Exam Study Guide MATH 140 - Recently Updated Verified

TAMU Final Exam Study Guide MATH 140 - Recently Updated Verified Matrix - answer - A matrix is often referred to by its size (dimensions): mxn. m (when thinking about the dimensions of a matrix) - answer - rows n (when thinking about the dimensions of a matrix) - answer - columns Find entry a23 in the following matrix: 1 3 5 4 5 7 9 11 17 - answer - 7 Square Matrix - answer - a matrix with the dimensions nxn; same number of rows and columns Row Matrix - answer - a matrix that has only one row with the dimensions 1xn (however many columns) Column Matrix - answer - a matrix that has only one column with the dimensions mx1 (However many rows) What comes first when describing matrix dimensions - answer - row comes first, then column Sum of two matrices - answer - given two matrices of the same size, one can add the corresponding entries of the two matrices. A+B=C How to put a matrix in calculator - answer - Alpha, zoom, enter the dimensions, input the data Check Answers on calculator - answer - If a matrix doesn't have variables you can check your work on the calculator Difference of two matrices - answer - Given two matrices of the same size, one can subtract the corresponding entries of the two (Don't do anything funky to try and make it work) A-B=C Commutative Property of matrices - answer - for all matrices mxn, A+B=B+A Associative Property of matrices - answer - for all matrices mxn, (A+B)+C=A+(B+C) Identity Property of matrices - answer - If 0mxn is the mxn matrix whose entries are all 0, then 0mxn(identity element) is called the mxn additive identity and for all mxn matrices A-- Doesn't change anything A+0mxn=0mxn+A=A Inverse Property of matrices - answer - For every mxn matrix A, there is a unique matrix denote -A, called the additive inverse of A (Answer will be the identity element) A+(-A)=(-A)+A=0mxn Multiplying a matrix by a scalar - answer - If A is any matrix and k is any number, the matrix is obtained from multiplying each entry of A by k (the resulting matrix (kA) will be the same size as A) Transposing a matrix - answer - Rows become columns and columns become rows, written as A^T Transposing matrix in calculator - answer - 2nd, matrix, math, 2nd option Transpose properties - answer - 1. If A is an mxn matrix, then A^T is an nxm matrix 2. (A^T)^T=A 3. (kA)^T=kA^T 4.(A+B)^T=A^T+B^T Matrix Equality - answer - Two matrices are equal if and only if: 1. They are the same size 2. Corresponding entries are equal Using matrices to solve real-world problems - answer - When using matrices to find solutions to real-world problems, begin by converting the info into a matrix using a logical system for the rows and columns (dimensions in the problem are a big clue as to how to set it up) Matrix Multiplication - answer - It is only possible when the INNER dimensions are the same (mxr)(rxm)=(mxm) *the 2 items leftover are the answer Matrix multiplication isn't... - answer - communitive, The order you multiply is very important Matrix Multiplication Process - answer - ROW BY COLUMN! 1. To obtain the entry in row 1, column 1 of AB, multiply the first row in A by the first column in B, and add 2. To obtain the entry in row 1, column 2 of AB, multiply the first row of A by the second column in B, and add 3. To obtain the entry in row 1, column 3 of AB, multiply the first row of A by the third column in B, and add Proceed the same way the same to obtain the second row of AB (row 2 of A times column 1 of B; row 2 of A times column 2 of B; row 2 of A times column 3 of B Properties of Matrix multiplication - answer - Matrix multiplication is not communititve but it is associative and distributive 1. Associative: (AB)C=A(BC) 2. Distributive: C(A+B)=CA+CB & (A+B)C=AC+BC * If it is in front it stays in front, if behind, it stays behind Cartesian Coordinate Plan - answer - a grid system having perpendicular axes X-axis - answer - the horizontal axis y-axis - answer - the vertical axis Center of the plane - a