Dimensions of Matrix

https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbY9EoNDZR-cVhnMwScyM2RheFb1v44Z38Yo1-2_w81guDVNFl6B3ZTWavWKJBhEngX-aI5-wKQB8Is2oh3bv9nnadWx4w0kD-QACm2W2tvWr1m-st7pCj_YROmQsVHWW0Cwwg3MIvo_4/s320/2x2_square.jpg

Thia ia a 2*2 MARIX

http://coachillclass-algii.blogspot.com/

1,3

https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWdztmPyGtWelN7_n_F_0Ke8G2Bvx1bOJWjV67yhwOB5Q0Y7tzwMB-U3qYTWXiUXvDcNYcoaDaTDIPcFbZDURl84k96q1ITeNOTEWAtuQba2qsOAtDWKoAmeKBxuY0xp1PqqgtfAKQQj8/s320/3x3_square.jpg

1,3

https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWdztmPyGtWelN7_n_F_0Ke8G2Bvx1bOJWjV67yhwOB5Q0Y7tzwMB-U3qYTWXiUXvDcNYcoaDaTDIPcFbZDURl84k96q1ITeNOTEWAtuQba2qsOAtDWKoAmeKBxuY0xp1PqqgtfAKQQj8/s1600/3x3_square.jpg

3,3

https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFilRGP49neAgDRYQLsh79i4v1vSXwwFaZTauDA7JFz3p0BpBWf0hbUCXVoOeHkZ7GZx064FT5yhrajwiFnJ3-LifieCmqu9bXJ-KkPz-yzmXRneiNVR09iTqNi-eU3rwXGglrRjDVVQA/s1600/3x2.jpg.

3,2

https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5BpPDvKKlNdqxYaYghLvdBIOePBlFv6cuMEgEUAPiR_eDAZQiHqxeN3ib4RsSNOUZFseAiq5GRUlXds1DYewqots3x9cb93vOll4ZLPxeTIBu3yme44-xq_V2B2M94cndUPwyEb7wCBw/s1600/3x3_indentity.jpg

3,3

Error Analysis

https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBuEjGM4eKWbMitwFPxma5zerReOCdH3uhCqs7NQVEbteXkNzvzQrjhVZlt7FnacxrjhqFZwgAtY3dbl3_eBwK-LLTgmvNolJOaPOOTRxgdI4oBtbHGWNAsQpRRmdvUw7YoKzMObbX31U/s1600/Page_4_Problem_9.jpg

Value of x is going up by 5 and the slope should be 10/5 or 2 not 10/1. Inserting the points, the final equation will be solved.  Y is not equal to 9+10x in the chart

https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghNQLHG6o9cST9mDIkoC671psI0OOdb3aafpdUWq7LCEB89yOfl_UI7SiztwvCGmdERKkRfD_W7VRfhQ__XRHMbs138ZvqDdDpfVZnvJSQMY2NJFPdO9wgXChsLlicBsYbFGAHZKPitdg/s1600/Page_8_Problem_16.jpg

To have a point it must try to solve both equations. So (1,2) only solves the first one and not the second one

https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHHwE-PSjRlFhywerLEnP98IAKsDXyu9J1-6UrJePYjL1zdcszsMT6jrubOwT9dY2LWwT1t7tcpqFeNrY335sMcFmgUCWE3Yvqsnhk_7yaZyoHS69BYPURJDx7o-UkoCAB1V_cJDxbxY8/s1600/Page_19_Problem_22_and_23.  

 20)shading is correct
  should be dotted line and not solid .
 #21 the solid line is correct, but the shading should be below the line, not above it.

https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtHC9QYK3cgnpvPGXc1n3WSjbApC0AIAg5V3L58TfaGgPPpq-M35QTjRAv6yWo_IPc-CDzIabtkn1nLNUIZRdUZYM36kygzU8JwAyAs1_IxSFff-UXf4NF-52CiNV9sEy11RPpYU_NHk4/s1600/Page_21_Problem_20_and_21.jpg

Graphing y=a|x-h|+k

y = a|x - h| + k

Although most books won't call the point (h,k) the vertex (as in quadratics) but it will either be a maximum or minimum value for the absolute value function.

If a > 0 , then (h,k) is the lowest point of the graph.  (opens upward)

If a < 0 , then (h,k) is the highest point of the graph.  (opens downward)

Types of Systems

Case 1	Case	Case 3

Independent system: one solution point	Case 2	Case 3

Independent system: one solution and one intersection point	Inconsistent system: no solution and no intersection point	Case 3

Independent  and consistent system: one solution and one intersection point	Inconsistent system: no solution and no intersection point	Dependent system: the solution is the whole line