find bases for the kernel and range of the linear transformations T in the indicated

Finite Mathematics Chapter 3 Section 1.1 Operations Identities 0 - Zero Addition/ Subtraction 1 - One Multiplication/ Division  Zero is the additive Identity as displayed above. You can add or subtract zero from any number without changing that number's value.  One is the multiplicative identity as displayed above. You can multiply or divide any number by one without changing that number's value. Functions can also: o Be added or subtracted: i.e. f(x) + g(x) o Multiplied or divided: i.e: f(x) * g(x) o Make composite functions: i.e fog(x) = f(g(x)) Inverses:  An inverse gets you back to the identity o Example: The additive inverse of 10 is –10 o Example: The multiplicative inverse of 4 is 4^-1 More Info:  If it is a function, it will pass the vertical line test  If it is an inverse, it will pass the horizontal line test There are three ways to define a line: 1. Slope-Intercept form ---> y= mx + b 2. Point-Slope Form --> y-y1 = m(x-x1) 3. 2 Points (x1, y1) (x2, y2) --> Slope: y2- y1 x2- x1 What is a matrix**  A rectangular block of numbers  The rows of a matrix can be: o Added o Multiplied by constants o Or switched Example of a Matrix: 1 1 3 1 -1 1 x + y = 3 x – y = 1 (the y's cancel when you add the equations together) 2x = 4 x = 2 (this gives you the x value in the coordinate) 1 1