2 Matrices notes 2018.notebook 1 October 04, 2018 (x+2) 2 x 2 when x=4 √32 (2)(3) 2
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2 Matrices notes 2018.notebook
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October 04, 2018
(x+2)2 x2 when x=4
√32
(2)(3)2
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Matrices
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• To add or subtract matrices, you must have the same dimensions
• What is A+B=
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Scalar Multiplication• Scalar Multiplication takes the elements of one matrix and multiplies it by some factor (not the same as multiplying one matrix by another)
• ½C=
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Try the following….
1. A+2B= 2. 3C4D= 3. 2A+3E= 4. 3D2C+4E=
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Matrix Multiplication• Used to multiply one matrix by another matrix—dimensions do not have to be the same (but the inside numbers have to match)
• EX. a 2X3 and a 3X4 can be multiplied together and the result will be a 2X4 (outside numbers)
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Multiplying Matrices
RS= SR=
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You try….
What is BA?
Is AB possible?
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Solving for unknowns in a matrix• Two matrices are equal if they have the same
dimensions and the corresponding entries are equivalent
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Solving systems with matrix equations• A financial manager wants to put $50,000 in an investment for a client, some in a low risk one earning 5% and some in a high risk one earning 14%. How much money should be invested at each interest rate to earn $5000 in interest per year?
• Set up system: Let x represent the amount in the low earning investment and y represent the amount in the high earning investment
• X+Y=50000• .05x+.14y=5000
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Set up Matrix equation
• If A represents the coefficients of your variables, X represents the variables, and B represents the constants, then…
• AX=B
• To solve for x, you would divide by A (which is the same as multiplying by the inverse)do this on both sides
• So x=A1B
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Solve this using matrix equations
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Solve using matrices
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