Solving Eq & Ineq        Graphs & Func.        Systems of Eq.        Polynomials        Frac. Express.        Powers & Roots        Complex Numbers        Quadratic Eq.        Quadratic Func.       Coord. Geo.        Exp. & Log. Func.        Probability    Matrices        Trigonometry        Trig. Identities        Equations & Tri. On this page we hope to clear up problems that you might have with matrices.  Matrices are good things to have under control and know how to deal with, because you will use them extensively in pre-calculus to solve systems of equations that have variables up the wazoo!  (Like one we remember with seven equations in seven variables.) Addition and subtraction Multiplication Quiz on Matrices To add matrices, we add the corresponding members.  The matrices have to have the same dimensions.  Example: ``` _ _ _ _ 1. Problem: | -5 0 | | 6 -3 | | | + | | |_ 4 1 _| |_2 3_| Solution: Add the corresponding members. _ _ | (-5 + 6) (0 - 3) | | | |_( 4 + 2) (1 + 3)_| _ _ | 1 -3 | | | |_6 4_| ``` Subtraction of matrices is done in the same manner as addition.   Always be aware of the negative signs and remember that a double negative is a positive! Back to Top  You can multiply a matrix by another matrix or by a number.  When you multiply a matrix by a number, multiply each member of the matrix by the number.  To multiply a matrix by a matrix, the first matrix has to have the same number of columns as the rows in the second matrix.   Examples: ``` _ _ 1. Problem: | -3 0 | 3| | |_ 4 5_| Solution: Multiply each member of the matrix by 3. _ _ | -9 0 | | | |_ 12 15 _| 2. Problem: Multiply the matrices shown below. _ _ _ _ | -2 1 || x | | || | |_ 4 -1 _||_ y _| Solution: Multiply the first member of each row in the first matrix by the top member of the column in the second matrix. Multiply the second members of the rows by the bottom member of the second matrix. _ _ | -2x y | | | |_ 4x -y _|``` Take the Quiz on matrices.  (Very useful to review or to see if you've really got this topic down.)  Do it!

Math for Morons Like Us - Algebra II: Matrices
/20991/alg2/matrices.html