Inverse Matrices

Subtraction is the inverse operation of Addition and Division is the inverse operation of

What size is this matrix?

• 2x2

• 2x3

• 3x2

• 1x6

What is the formula for the determinant of a 2x2 matrix?

• ad-bc

• ab-cd

• ad+bc

• (a+d)(b+c)

What is A^-1?

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What is the inverse of this matrix?

• _{(2/30)  (-5/30)
  (4/30)  (16/30)}

• _{(1/25)  (-4/25)
  (3/25)  (13/25)}

• _{(7/30)  (-3/30)
  (1/30)  (10/30)}

• _{(2/300)  (-5/300)
  (4/300)  (16/300)}

Identify the coefficient matrix for the following system.

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Write the matrix equation for the system.

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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

Let's dive into a matrix mystery! 🕵️‍♂️ Can you tell if A and B are inverse partners in crime? 
A = ⌈3  -10⌉
        ⌊1      4⌋
B = ⌈2/11  5/11⌉
         ⌊-1/22   3/22⌋
*Hint: AB should equal the identity matrix (I) for them to be inverses.*

• Yes, they are inverses!

• No, they're just acquaintances.