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Published byElwin Jordan Modified over 9 years ago
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4.1 An Introduction to Matrices Katie Montella Mod. 6 5/25/07
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Matrices A matrix is just a rectangular array of numbers. Now you need to know about rows and columns.
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Rows and Columns Rows go this way Columns go this way
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Sample Problem [ 5x ] = [ y ] [5x + 4y] [10] You want to solve for x and y Since the matrices are equal, the corresponding elements are equal. 5x = y 5x + 4y = 10
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Sample Problem The first equation gives a value for y that can be substituted into the second equation to find the value of x. 5x + 4y = 10 5x + 4(5x) = 10 5x + 20x = 10 25 = 10x x = 2/5
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Sample Problem To find the value of y, substitute 2/5 into either equation. 5x = y 5(2/5) = y 2 = y The solution is (2/5, 2).
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Practice Problems 1.) [2x] = [40 + 2y] [ y ] = [ 5 – 4x ] Try to solve this problem by yourself.
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#1 work 2x = 40 + 2y y = 5 – 4x
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#1 work 2x = 40 + 2(5 – 4x) 2x = 40 + 10 – 8x 2x = 50 – 8x 2x + 8x = 50 10x = 50 x = 5
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# 1 Work y = 5 – 4x y = 5 – 4(5) y = 5 – 20 y = -15 Solution is (5, -15).
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Practice Problems 2.) [ 2x ] = [ y ] [2x + 3y] = [12] Try to solve this by yourself.
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#2 Work 2x = y 2x+ 3y = 12
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# 2 Work 2x +3(2x) = 12 2x + 6x = 12 8x = 12 x =1.5
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# 2 Work 2x = y 2(1.5) = y 3 = y The solution is (1.5, 3).
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The End.
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