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Unformatted text preview: 42 Matrices and Systems of Linear EquationsHere is a system of 3 equations with 3 unknowns:x  2y + 3z = 9(R1)x + 3y= 4(R2)2x  5y + 5z= 17(R3)•we will not be writing such a system in the usual way•there's an easierway to record and manipulate it . . . •as a matrix(the augmented matrixof a system):3 rows1755243193214 columnsan example of a (3 x 4) matrix (3 rows by 4 columns).A matrixis a rectangular array of numbers.col col col12 3 312531= 232221131211aaaaaarow dimension: 2column dimension: 3dimensionsof matrix: 2 ×3 ("two by three")a square matrixhas the same number of rows as columns42p. 1each elementhas a name:row 1 row 2 Consider this system of equations (we will refer to the equationsas rowsin accordance with the augmented matrix representation of a system):Row 1:2x + 4y + 4z = 4Row 2:x + 3y + z = 4Row 3:x + 3y + 2z = 11. If we interchange two rows, will that affect the...
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 Spring '11
 Staff
 Linear Algebra, Linear Equations, Equations, Multiplication, Matrices, Systems Of Linear Equations, Elementary algebra, Elementary matrix

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