- WELCOME TO A VIDEO THAT WILL SHOW
HOW TO CONVERT AUGMENTED MATRICES INTO ROW ECHELON FORM
AND REDUCED ROW ECHELON FORM
USING THE TI83 OR 84 GRAPHING CALCULATOR.
SO THE PREVIOUS VIDEOS SHOWED
HOW TO SOLVE A SYSTEM OF EQUATIONS BY HAND
IN ROW ECHELON FORM AND REDUCED ROW ECHELON FORM
AND NOW WE'LL SHOW HOW TO CHECK IT ON THE GRAPHING CALCULATOR.
SO THE FIRST THING WE HAVE TO DO IS GET OUR CALCULATOR OUT.
TO ENTER THE MATRIX MENU WE PRESS 2nd X TO THE POWER OF -1
AND THEN WE'LL GO OVER TO THE EDIT MENU
SO HIT YOUR RIGHT ARROW TWICE AND THEN PRESS ENTER.
SO MATRIX "A" WILL BE THE AUGMENTED MATRIX FOR THIS SYSTEM
SO IT WILL BE A 2 BY 3 MATRIX.
SO WE PRESS 2 ENTER, 3 ENTER
AND THEN WE JUST TYPE IN THE ELEMENTS.
SO WE'LL HAVE 2, -3, 18 IN THE FIRST ROW.
THE SECOND ROW WILL BE 5, 2, AND 7.
THAT'S PRETTY MUCH ALL WE NEED TO DO.
NOW WE CAN GO BACK TO THE HOME SCREEN,
PRESS 2nd MODE OR 2nd QUIT
AND THEN WE'RE GOING TO GO BACK TO THE MATRIX MENU
SO WE'LL PRESS 2nd X TO THE POWER OF -1.
NOW WE'LL SCROLL OVER ONE TIME TO THE MATH MENU
AND LET'S GO AHEAD AND CONVERT THIS AUGMENTED MATRIX
INTO ROW ECHELON FORM.
SO WE'LL SCROLL DOWN TO OPTION "A" WHICH IS REF, PRESS ENTER.
IT BRINGS IT BACK TO THE HOME SCREEN
NOW WE HAVE TO SELECT MATRIX "A."
SO WE PRESS 2nd MATRIX
AND THEN SELECT MATRIX "A," CLOSED PARENTHESES
AND THEN PRESS ENTER.
NOW NOTICE IT'S IN DECIMAL FORM.
THIS IS ROW ECHELON FORM.
WE HAVE A MAIN DIAGONAL OF 1'S AND A ZERO
BELOW THE MAIN DIAGONAL.
WE CAN PRESS MATH, ENTER, ENTER
TO CONVERT IT TO DECIMAL NOTATION IF WE WISH.
SO REMEMBER THIS TELLS US THAT X + 2/5Y = 7/5 AND THAT Y = -4.
BUT IT'S JUST AS EASY TO CONVERT THIS
INTO REDUCED ROW ECHELON FORM ON THE GRAPHING CALCULATOR
BECAUSE NOTICE HERE WE STILL HAVE TO GO BACK
AND SOLVE IT ALGEBRAICALLY.
SO LET'S SHOW HOW TO CONVERT THIS
TO REDUCED ROW ECHELON FORM AS WELL.
WE'LL PRESS 2nd MATRIX.
GO OVER TO THE MATH MENU
AND NOW WE'LL LOOK FOR REDUCED ROW ECHELON FORM
WHICH IS RIGHT BELOW ROW ECHELON FORM.
SO OPTION B IS RREF.
WE CAN PRESS ENTER AND NOW SELECT MATRIX "A" AGAIN.
SO 2nd MATRIX, PRESS ENTER, CLOSED PARENTHESES
AND PRESS ENTER AND NOW WE KNOW THAT X = 3 AND Y = -4.
LET'S GO AHEAD AND TRY A SYSTEM OF THREE EQUATIONS
WITH THREE UNKNOWNS WHILE WE'RE HERE.
SO WE'LL ENTER IN THIS AUGMENTED MATRIX AS MATRIX B.
SO PRESS 2nd, MATRIX, GO OVER TO EDIT
AND NOW WE'LL SCROLL DOWN TO MATRIX B, PRESS ENTER.
SO THIS AUGMENTED MATRIX WOULD BE A 3 BY 4
AND THEN WE JUST ENTER IN THE ELEMENTS SO WE HAVE 1, -1, 1, 2.
ROW 2 WOULD BE 3, -2, 1, -1,
AND THE LAST ROW IS MISSING A Z TERM
SO WE'D HAVE 1, 1, 0 FOR 0Z AND THEN -3.
WE'LL GO BACK TO THE HOME SCREEN, 2nd, QUIT
AND AGAIN WE'LL GO AHEAD AND SHOW IT IN ROW ECHELON FORM
BUT IT'S GOING TO BE MUCH EASIER TO FIND THE SOLUTION
IN REDUCED ROW ECHELON FORM.
SO NOW WE'LL GO BACK TO THE MATRIX MENU, 2nd, MATRIX,
RIGHT ARROW ONCE TO THE MATH MENU
AND THEN WE'LL SCROLL DOWN TO OPTION "A" FOR REF
OR ROW ECHELON FORM.
PRESS ENTER, SELECT MATRIX B.
SO 2nd MATRIX, SCROLL DOWN ONCE, ENTER,
CLOSED PARENTHESES, PRESS ENTER
AND AGAIN NOTICE HOW WE'RE GOING TO HAVE SOME FRACTIONS HERE.
SO LET'S PRESS MATH, ENTER, ENTER
AND THERE IS SOME MORE INFORMATION
TO THE RIGHT OF SCREEN.
IF YOU PRESS THE RIGHT ARROW YOU CAN GO OVER THERE AND SEE IT.
SO AGAIN, IN ROW ECHELON FORM WE'D STILL HAVE TO GO BACK
AND PERFORM BACK SUBSTITUTION
TO DETERMINE THE VALUES OF X, Y, AND Z.
LET'S GO AHEAD NOW AND SHOW IT IN REDUCED ROW ECHELON FORM.
SO WE'LL PRESS 2nd, MATRIX, RIGHT ARROW TO MATH
AND THEN OPTION B WHICH IS RREF FOR REDUCED ROW ECHELON FORM,
PRESS ENTER.
NOW WE'LL SELECT MATRIX B, 2nd MATRIX,
SCROLL DOWN ONCE TO MATRIX B, PRESS ENTER, CLOSED PARENTHESES
AND THEN ENTER.
SO THIS IS MUCH EASIER TO SEE AS WELL
BUT NOW WE KNOW THAT X = -2, Y = -1, AND Z = 3.
THAT'LL PRETTY MUCH DO IT FOR THIS VIDEO.
HOPEFULLY, YOU'VE ALREADY WATCHED THE OTHER VIDEOS
THAT SHOW YOU HOW TO DO IT BY HAND
BECAUSE REALLY ON THE CALCULATOR WHAT WE'RE DOING
IS JUST PUSHING BUTTONS.
IT DOESN'T REALLY DEMONSTRATE MUCH OF AN UNDERSTANDING
OTHER THAN TO INTERPRET THE END RESULT.
SO I HOPE YOU FOUND THIS HELPFUL AND THANK YOU FOR WATCHING.