Ch' 4'5: Identity and Inverse Matrix

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Ch. 4.5 Identity and Inverse Matrix
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Identity Matrix

• For a 2x2 matrix, it is always
• Matrix must be SQUARE (IE 2x2, 3x3,etc)
• For a matrix A, A-1A I

Inverse Matrix
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To find the Inverse of a 2x2 Matrix M, if M

• 1) Find the determinant of the M
• If it is 0, then the answer is NOT POSSIBLE
• 2. The inverse matrix
• 3. To check, Multiply A-1A and see if it becomes
  the identity matrix

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Ex Find the inverse matrix, if possible

• Answer Not Possible
• because it is not square

Answer Not Possible because the
determinant equals 0
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Ex Find the inverse matrix, if possible

• Determinant 16-20 -4, so it is possible!
• Plug into inverse format

• A-1A I , so is the inverse

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Ex Find the inverse matrix, if possible

• Determinant 8-6 2, so it is possible!
• Plug into inverse format

• A-1A I , so is the inverse