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TTU - MATH 1330 - Study Guide - Midterm

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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 #

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

⎣⎦ ⎣⎦

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• 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