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# Matrices Chapter 4 Obj. 1.04,2.10

## by jeaniehenschel on Feb 08, 2011

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## Matrices Chapter 4 Obj. 1.04,2.10Presentation Transcript

•  Matrix Matrix element Row Column Zero matrix Equal matrices Corresponding elements Scalar Scalar multiplication
•  Rows x columns Read rows by columns Rows go across Columns go down [ 1 2 3 4 ] 1 x 4 matrix
•  Element A 13 Means the term in the 1st row , 3rd column A 13 = 3
•  Matrices can be used to organize and compare statistical data.
•  Three students kept track of the games they won and lost in a chess competition. # = won - = loss Ed # - # # - ## Jo ####-## Lou -#--##-
•  You can add or subtract matrices to get new information. You must have matrices with equal dimensions. You will combine corresponding elements.
•  MATRX Over 2 EDIT ENTER Put in the size of the matrix Remember rows x columns Press ENTER after each element 2nd QUIT
•  Be sure to enter the matrices into the calculator as they are given in the problem.
•  Enter matrices as given in the problem. 2nd QUIT MATRX select Matrix A Then enter operation symbol MATRX select Matrix B ENTER, record the answer
•  Same process as solving linear equations Isolate the variable Use inverse operation Solve
•  X - [ 1 1]= [0 1] [ 3 2] [ 89]Enter the 2nd matrix as A since it is not going to move.Enter the 1 matrix as B. st
•  Same number of rows Same number of columns Corresponding elements are equal
•  [4] [3 4 7 ] [6] [8]Equal matrices?Why or why not?
•  [ -2 3 ] [ -8/4 6-3 ] [ 5 0] [ 15/3 4-4]Equal matrices?Why or why not?
•  Since the two matrices are equal, their corresponding elements are equal. Set up equations using corresponding elements Solve for the variable
•  [x+8 -5 ] = [ 38 -5 ] [ 3 -y ] [3 4y-10]
•  x + 8 = 38 -y = 4y – 10 - 8 -8 -4y -4y x = 30 -5y = -10 y=2
•  [ 3x 4] = [ -9 x +y]
•  Matrix multiplication is not commutative. Order matters!
•  Scalar is the number on the outside of the matrix. Multiplying by a scalar is just like distributive property.
•  Enter matrix into calculator in matrix A. 2nd QUIT Enter scalar, then choose matrix A ENTER Record answer
•  3[2 6] [7 4]
•  5A – 3B A + 6B 5B – 4A
•  Just like solving equations with distributive property To eliminate a scalar that is a fraction….multiply by the reciprocal
•  -3y + 2 [ 6 9 ] = [ 27 -18 ] [ -12 15] [ 30 6 ]
•  2x = [ 4 12 ] + [ -2 0] [ 1 -4] [ 3 4]
•  -3x + [ 7 0 -1 ] = [ 10 0 8] [2 -3 4] [-19 -18 10]
•  Product exists only if The number of columns of A EQUALS The number of rows of B
•  Determine dimensions of each matrix Determine dimension of product matrix Check to see if # of Col. Of A equals # of rows of B If yes = product defined If no = product undefined Undefined means does not exist.
•  The number of rows of matrix A By The number of columns of matrix B
•  If the number of columns of A does not equal the number of rows of B….. The calculator will give you an error message.
•  [ -2 5] [ 4 -4 ] [3 -1] [2 6] A has 2 rows and 2 columns. B has 2 rows and 2 columns.The col. Of A = the rows of
•  [ 10 ] [ 12 3] [ -5 ][1 2] [ 7 6 8 13 ][3 4] [ 9 10 11 19]
•  [ w x ] [ 9 -7 ] [ y z ] [3 1] [ -3 5] [ -3 ] [ 5]