PPT-8.5.3 – Unit Vectors, Linear Combinations

In the case of vectors we have a special vector known as the unit vector Unit Vector any vector with a length 1 direction irrelevant Two special unit vectors we look at the most i 1 0. e Ax where is vector is a linear function of ie By where is then is a linear function of and By BA so matrix multiplication corresponds to composition of linear functions ie linear functions of linear functions of some variables Linear Equations Statistics group. Axelborg. 16/01 2012. Anders . Stockmarr,. DTU Data Analysis. Joint work with . Peter Heegaard . and . Nanna Skall Sørensen. Acute Phase Proteins – APP’s:. Proteins whose plasma concentrations . Section 6.3. Section Summary. Permutations. Combinations. Combinatorial Proofs. Permutations. Definition. : A . permutation. of a set of distinct objects is an ordered arrangement of these objects. An ordered arrangement of r elements of a set is called an . A . scalar. quantity . can be described by a . single number. , . with some meaningful . unit. 4 oranges. 20 miles. 5 miles/hour. 10 Joules of energy. 9 Volts . Vectors and scalars. A . scalar. quantity . Other Counting Tools: Factorials. MATH 110 Sec 12-3 Lecture: Permutations and Combinations . Other Counting Tools: Factorials. Sometimes we are interested in counting the number of different arrangements of a group of objects.. David Plaxco. Linear Independence of Functions. Definition of linear independence of vector-valued functions. :. Let . f. i. : . I . = (. a,b. ) . → . . . n. , . I = 1, 2. ,…. , n. .. . The . Other Counting Tools: Factorials. MATH 110 Sec 12-3 Lecture: Permutations and Combinations . Other Counting Tools: Factorials. Sometimes we are interested in counting the number of different arrangements of a group of objects.. . example:. ..  .  .  . where . are unit vectors in x, y and z directions..  . .  .  .  .  . Both, position vector of point A and point A have the same coordinates:. Vector as position vector of point A in . Statistics group. Axelborg. 16/01 2012. Anders . Stockmarr,. DTU Data Analysis. Joint work with . Peter Heegaard . and . Nanna Skall Sørensen. Acute Phase Proteins – APP’s:. Proteins whose plasma concentrations . Random Things to Know. Dice. . (singular = “die”). Most cases: 6 sided. Numbers 1,2,3,4,5,6. Special Cases: . 4 sided. 8 sided. 10 sided. 12 sided. 20 sided.  . Random Things to Know. Cards. Typical Deck: 52 cards. GPS: What is it?. GPS is the Graduation Planning System. It will provide students with a clear and direct path to degree completion. GPS Website – . http://www.kent.edu/gps. 2. GPS – Major Components. Any vector can be resized by multiplying it by a real number (scalar).. Multiplying by positive scalar changes magnitude only.. Multiplying by a negative scalar changes the magnitude and its direction.. properties, addition, components of vectors . When you see a vector, think components!. Multiplication of vectors will come in later chapters.. Vectors have . magnitude. and . direction. .. Chapter 3: Vectors. A curve showing the combinations of factor inputs that have constant market cost. If firms are acting as price-takers in factor markets, the iso-cost curve is a straight line, whose slope represents the relative prices of different factors' services..