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Notes: Using Matrices to Represent DataWe can also use a _________________ to display data. A matrix is arranged in rows and columns. The ______________________ of a matrix are the number of rows by the number of columns. Each value in a matrix is called an ____________________ of the matrix. Example; represent the data as a matrix and identify the dimension In the 1st grade class there are 13 who prefer strawberry ice cream, 4 like chocolate, and 8 like butter scotch ice cream. The 2nd grade class has slightly different taste; 7 like strawberry, 12 prefer chocolate, and 9 like butter scotch. Example; represent the data as a matrix and identify the dimension A washing machine company collects data on the sales of machines in three cities from year 2002 to 2005. The results showed that in City A: 70, 74, 85, 90; City B: 54, 65, 72, 83; and City C: 105, 99, 85, 76.Notes: Properties of Matrix OperationsMatrices have some special properties we need to know before we can actually perform operations. Recall that when identifying the size (dimension) of a matrix, it is the number of rows by the number of columns. To multiply a matrix by a constant (scalar): ______________________________________________________ To add or subtract two matrices: ___________________________________________________________________ To multiply two matrices: __________________________________________________________________________Example; identify the size of the matricesB=213+050-100C=4863-302715D=44-10132+12101248C=4863302715D=44-10132101248Notes: Multiplying Matrices by ScalarsYou can multiply a matrix by a number, called a ____________________________________To find the product of a scalar and a matrix or the scalar product, multiply each entry by the scalar. Examples; find the scalar productsP=3-2102-1, Q=47251-1, R=14-23043P12R -4QNotes: Add, Subtract, and Multiply MatricesAdd or subtract the corresponding parts of the matrices. You can add or subtract two matrices only if they have the same __________________. You will get a matrix with the same dimensions. Examples; find matrix sums and differencesW=3-210, X=47251-1,Y=14-23, Z=2-23104W+Y= X-Z= X+Y= It is possible multiply matrices together. The product of two or more matrices is the matrix product. The following rules apply when multiplying matrices. The number of _________ in the 1st= the number of ________ in the 2ndP=a1a2b1b2c1c2d1d2= Example; find the matrix productsW=3-2102-1, X=47251-1, and Y=14-23XW= XY= ................
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