Matrices

Mrs Lenox Math Help: Matrices

Dimensions,Element Location

Matrix Terms
jmatrix

For dimensions and element location, writerow then column.

J is 3 x 5. J23=4. J13=14.

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Add Subtract

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jmatrix

Elements in the same row,column location combine, and that number is placed in the answer matrix in that row column location.
Note: If both matrices don't have the same dimensions,the operation is undefined.

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Scalar Multiplication

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jmatrix

Multiply each element by the constant out front. think: distribution

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Multiplication

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jmatrix

To multiply, start at the left element in the row you need and the top element in the column you need. Multiply those together. Keep going.Add all the products together. Place that number in the matching row column of the product matrix.Note: If the number of columns in the first matrix doesn't match the number of rows in the second, they cannot be multiplied together.

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Encode a message

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jmatrix

Convert letters to number equivalent. I'll do HELP, which is 8 5 12 16. Organize that into a matrix with the same number of columns as the key matrix dimension. I'll use a 2 by 2 key, so my message is in a 2 column matrix. Multiply the message times the key to encode the message. In this example: 34 47 68 96.

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Decode a message

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jmatrix

Organize the encoded message into a matrix with the same number of columns as the key. Multiply that by the inverse of the key matrix and you will have the original message back. Here, 8 5 12 16.

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Solve systems

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jmatrix

To write the augmented matrix,each row is an equation. Each column gets the coefficient of a single variable (first column x's, second column y's,etc). If a variable is not in the equation, put a zero as the coefficient. The rref command on the calculator will provide reduced row echelon form of the augmented matrix.

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Solve systems:Row Echelon Form and Back Substitution

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jmatrix

To get the reduced echelon form, use ref in the math menu of matrix. To solve, start at the bottom. Here, z = 5. Then substitute the 5 in for z in the equation above it. Here, y + 2(5)=13. That will allow you to solve for y. Then substitute the number values for y and z into the top equation to solve for x. You should get x=6, y=3 and z=5 for this example.

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Practice Problems

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