MATH 140 Exam 1 – Practice Questions with Complete Solutions

Texas A & M University-College Station MATH 140


MATH 140 EXAM 1 QUESTIONS WITH COMPLETE SOLUTIONS


What are the dimensions of a matrix? rows x columns


In order to add/subtract two matrices which of the Both matrices must have the same dimension/size.
following must be true?


Commutative Property A+B = B+A (order doesn't matter)


Associative Property (A+B)+C = A+(B+C)


Identity Property A+0(mxn) = 0(mxn)+A = A
- additive identity: the matrix made up of zeros that when added to matrix A =
matrix A


Inverse Property A+(-A) = (-A)+A = 0
- additive inverse: the matrix, that when added to matrix A, results in a matrix of
zeros


transpose take the rows and make them into columns


Matrix multiplication ORDER MATTERS!
ex: (3x2)(2x3) --> can multiply because middle two dimensions (2 and 2) are the
same --> leads to resulting matrix of a (3x3)


slope m = rise/run


equation and slope of a vertical line equation: x = ?
slope: m = rise/run = infinity/0 = undefined


equation and slope of a horizontal line equation: y = ?
slope: m = rise/run = 0/infinity = 0


Standard Form Ax + By = C
1.) find slope-int. form
2.) move x and y to one side
3.) get ride of any fraction/decimals


Linear Depreciation (t , v)
V(t) = mt + b
*m = rate of change = change in V/change in t


Rate of Depreciation the amount of value an asset loses per time unit
[m] (pretend that is the absolute value of m)
*always positive




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