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Unformatted text preview: 4-2 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 waythere's an easierway to record and manipulate it . . . as a matrix(the augmented matrixof a system):3 rows----1755243193214 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 columns4-2p. 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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