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TTU / Mathematics / MATH 1330 / How do you do scalar multiplication?

# How do you do scalar multiplication? Description

##### Description: These notes cover the equations from chapter 3 and 6
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If you want to learn more check out When the hairpin loop forms on the strand of mrna, what happens to the transcription?

Midterm 2 Study Guide (CH 3 and 6)

• Matrices: classified in terms of numbers of rows and columns they have - m rows and n columns ⇒ Don't forget about the age old question of What is the most common definition of a felony?

• Sum of matrices: the sum of is a matrix C whose elements are

• Scalar multiplication:  multiplying a matrix by a real at number (called a scalar) results in a matrix in which each entry of the original matrix is multiplied by the real #

We also discuss several other topics like What are the objectives of an association as defined in the charter?

A =         ⎡⎤  then CA =         ⎡⎤Don't forget about the age old question of Are there distinct processing systems used for object recognition?

⎣⎦                ⎣

If you want to learn more check out What is the ebbinghaus learning curve?

• Product of two matrices: given an A and anB, the matrix product AB is an CDon't forget about the age old question of What are the aspects of development?

EX:

Final AB if A =        ⎡3 4⎤         B =        ⎡a b c d⎤ ⇒        ⎡3a+4e     3b+4f     3c+4g     3d+4h  ⎤

⎢2 5⎥                ⎣e f g h ⎦        ⎢2a+5e     2b+5f     2c+5g     2d+5h  ⎥

⎣2 4⎦                                ⎣6a+10e   66+10f   6c+10g   6d+10h⎦

• Identity matrix: a square  that has 1s down its diagonal and 0s everywhere else

I =        ⎡1 0 0⎤

⎢0 1 0⎥

⎣0 0 1⎦

• Augmented matrix: the numbers on the left side of the solid line from the coefficient matrix with each column containing the coefficients of a variable

Ex:        ⎧        ⎡1 2   3|6⎤

⎢1 0  -1|0⎥

⎣1 -1 -1|4⎦

• Elementary row operations:

(1) interchange two rows

(2) add a multiple of one row to another row

(3) multiply a row by a nonzero constant

• Inverse matrices: two square matrices, A and B, are called inverses of each other if and  ⇒

• Inverse at a 2x2 matrix:       if A=        ⎡a b⎤, then

⎣c d⎦

• Determinant of a 2x2 matrix:

⎡a b⎤ =        ⎡a b⎤ =

⎣c d⎦        ⎣c d⎦

Ex:

⎡2  4⎤ ⇒

⎣3 -4⎦

• Open Leontief Model: the technological equation for an open leontief model is

• A is the technology matrix -x is the gross production matrix
• D is the final demands matrix
• This is called an open model because some of the goods from the economy are “open” or available to those outside the economy

• Closed Leontief Model: if a model is developed in which all inputs and outputs are used within the system

Chapter 6

• Simple Interest:

• Future value: the future amount of an investment at the end of an interest period is the sum of the principal and the interest

• The principal at an investment is also called present value

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