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If the determinant is equal to 0, there is no inverse matrix

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This video will help you better understand how to add vectors and graph them together

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Adding vectors | Vectors and spaces | Linear Algebra | Khan Academy

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[3 5]
[2 4]
3(4)-5(2)=
12-10= 2
1/2 [4 -5]  =  [2 -5/2]
[-2 3]  = [-1 3/2]

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The equation is STRETCHED if it's multiplied by a whole number (ex: 1, 4, 19)
The equation is SHRINKED if it's multiplied by a fraction (ex: 1/2, 2/5)

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The area is the absolute value of the determinant:
/ad-bc/

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-When a vector represents a moving object, its speed is found by calculating its magnitude (distance)
-To calculate speeds together add the vectors together first and then calculate magnitude

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Refeltion over y-axis: [-1 0]
[0  1]
Reflection over x-axis: [1 0]
[0 -1]
90* Rotation CC: [0 -1]
[1  0]
180* Rotation CC:  [-1 0]
[0 -1]
270* Rotation CC: [0 1]
[-1 0]

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Parallelograms: opposite sides are parallel (slope) and opposite sides are congruent
Rectangle: Opposite sides are congruent and consecutive sides have opposite reciprocal slopes (perpendicular)
Rhombus: all sides are congruent and opposite sides are parallel
Square: All sides are congruent and consecutive sides are opposite reciprocal slopes

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-If outside the parentheses then it affects the y
-If inside the parentheses then it affects the x and it may be opposite as well

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Additive Identity (when added to matrix you get out the same matrix): [0,0]
[0,0]
Multiplicative Identity (when you multiply a matrix you get the same one) [1,0]
[0,1]
Finding Multiplicative Inverse (to find inverse matrix- when multiplied by matching matrix you get the multiplicative identity):
1/determinant [d -b]
[-c a]
Finding the Determinant (so you can find determinant-tells if the matrix has an inverse): ad-bc
Solving Matrix Equations (to simplify matrix): [a b] [x] = [e]
[c d]  [y] = [f]