Systems Pre-Assessment

Solving Systems:
Solve for x and y
3x + 2y = 16
7x + y = 19

• (-2,5)
• (-2,-5)
• (2,-5)
• (2,5)

Tags

CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.11

System of inequalities:
Which system is pictured?

• y > -2 + x
  y ≤ 2x + 2
• y > 2 + x
  y ≤ 2x + 2
• y ≥ -2 + x
  y ≤ 2x + 2
• none of these are the system

Systems of 3 Equations:
-x+6y-z=6
2x+y-3z=16
-x+5y+3z=-7

• A (0, -6, 0)
• B (0, 0, -6)
• C (3, 1, -3)
• D (-6, 4, -3)

Tags

CCSS.HSA.REI.C.6

Matrix operations:
What must be true in order to ADD two matrices?

• They must be square.
• The dimensions must be equal.
• The determinant can't equal 0.
• The column of the 1st must equal the row of the 2nd.

Matrix Operations:
Find B-A

• -3     1
  7     -1
• 1     0
  1     -4
• -4       0
  6     -1
• not possible because rows do not match columns

Matrix Operations:
You can multiply a 2X3 matrix by which matrix?

• 2X2
• 2X12
• 3X12
• 2X3

Matrix Operations:
find: B*A

• 47     30
  9     5
• 17     15
  42     35
• 10     25
  7     1
• not possible because rows do not match columns

Determinants:
Find the determinant of matrix A.

• 10
• not possible
• 14
• -14

Solving using Matrices:
When solving a system AX=B using inverse matrices, you use the equation:

• X=A^-1B
• B=X^-1A
• A=X^-1B
• X=B^-1A

Matrix Inverses:

• 5   -2
  -3    1
• -5   2
  3   -1
• -5   3
  2   -1
• 1   -3
  -2    5