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- WELCOME BACK.
TODAY WE'RE GOING TO TAKE A LOOK
AT HOW TO FIND THE INVERSE OF A 2 X 2 MATRIX
USING A SPECIFIC FORMULA.
SO IF WE HAVE MATRIX A IN THIS FORM
THEN A INVERSE WILL = 1 DIVIDED BY AD - BC
x THE MATRIX
IN WHICH WE INTERCHANGE THE POSITION OF A AND D.
SO INSTEAD OF A BEING HERE AND D BEING HERE,
WE'D PUT D HERE AND A HERE.
AND THEN B AND C STAY IN THE SAME POSITION,
BUT WE TAKE THE OPPOSITE SIGN.
AND THIS WILL WORK FOR A 2 X 2 WHEN AD - BC DOESN'T = 0.
SO LET'S GO AHEAD AND GIVE IT A TRY.
SO A INVERSE SHOULD = 1 DIVIDED BY AD - BC.
SO AD WOULD BE -5 x 3 OR -15 - BC OR -3 x 4
THAT'S -12 x THE MATRIX
WHERE WE CHANGE THE POSITION OF A AND D.
SO THIS WOULD BE A 3 AND THIS WOULD BE A -5.
AND THESE TWO ELEMENTS STAY IN THE SAME POSITION
BUT WOULD TAKE THE OPPOSITE SIGN.
SO THIS WOULD BE A +3 AND THIS WOULD BE A -4.
LET'S GO AHEAD AND SIMPLIFY THIS.
-15 + 12 IS GOING TO BE -3,
SO WE HAVE -1/3 x THE MATRIX 3, 3, -4, -5.
LET'S GO AHEAD AND PERFORM THIS SKIT IN MULTIPLICATION.
SO THE INVERSE MATRIX WOULD BE -1/3 x 3 THAT'S -1,
THIS WOULD ALSO BE -1.
THIS SHOULD BE 4/3 AND THIS WOULD BE 5/3.
SO IF THAT IS THE INVERSE MATRIX
THEN WE KNOW FROM OUR PREVIOUS VIDEO
THAT A x A INVERSE SHOULD BE THE IDENTITY MATRIX.
AND A INVERSE x A SHOULD ALSO = THE IDENTITY MATRIX.
LET'S GO AHEAD AND CHECK THIS ON THE GRAPHING CALCULATOR.
SO LET'S PRESS SECOND MATRIX, GO OVER TO EDIT,
AND WE'LL ENTER IN MATRIX A AS A 2 X 2,
SO WE'D HAVE -5, ENTER, -3, ENTER, 4, ENTER, 3, ENTER.
AND THEN WE'LL LET MATRIX B = THE INVERSE MATRIX.
SO WE HAVE -1, -1, 4/3, AND 5/3.
OKAY. LET'S GO AHEAD AND GO BACK TO THE HOME SCREEN.
AND LET'S JUST MAKE SURE
THAT A x B AND B x A DOES = THE IDENTITY MATRIX.
SO PRESS SECOND MATRIX A x SECOND MATRIX B, ENTER, ENTER,
AND THIS CHECKS OUT.
AND LET'S GO AHEAD AND CHECK B x A.
AND IT WORKS.
SO THIS IS A VERY CONVENIENT FORMULA
FOR FINDING THE INVERSE OF A 2 X 2 MATRIX
IF THE MATRIX DOES HAVE AN INVERSE.
AND THAT'LL DO IT FOR THIS VIDEO.
THANK YOU FOR WATCHING.