Hi! Given: w 1 = 5 x 1 - x 2 + x 3 w 2 = - x 1 + x 2 +7 x 3 w 3 = 2 x 1 -4 x 2 -

Question

Hi! Given: w1 = 5x1 -x2 + x3 w2 = -x1 +x2 +7x3 w3 = 2x1 -4x2 - x3                                                                                                   T I need to find the domain and codomain of the transformationsx----->w defined by theequations, and determine whether T is linear. If you could please help at all, please list the steps and/orexplain. Thanks so much!! Hi! Given: w1 = 5x1 -x2 + x3 w2 = -x1 +x2 +7x3 w3 = 2x1 -4x2 - x3                                                                                                   T I need to find the domain and codomain of the transformationsx----->w defined by theequations, and determine whether T is linear. If you could please help at all, please list the steps and/orexplain. Thanks so much!!                                                                                                   T I need to find the domain and codomain of the transformationsx----->w defined by theequations, and determine whether T is linear. If you could please help at all, please list the steps and/orexplain. Thanks so much!!

Explanation / Answer

Hi! Given: w1 = 5x1 -x2 + x3 w2 = -x1 +x2 +7x3 w3 = 2x1 -4x2 - x3                                                                                                   T I need to find the domain and codomain of the transformationsx----->w defined by theequations, and determine whether T is linear. If you could please help at all, please list the steps and/orexplain. Thanks so much!!
DOMAIN IS THE SET OF VALUES OF X WHICH MAKE THE TRANSFORM
OPERATION MATHEMATICALLY PERMISSIBLE.
SINCE ALL RELATIONAL EQNS OF TRANSFORMATION ARE LINEAR COMBINATIONSOF DIFFERENT REAL NUMBERS WHICH DO NOT INVOLVE ANY IN-PERMISSIBLEOPERATION
LIKE DIVISION BY ZERO ETC...
THE DOMAIN IS ALL REAL NUMBERS FOR X ..THAT IS X CAN TAKE ANY REALVALUE.
CO - DOMAIN IS ALL THOSE VALUES OF W WE GET BY ASSIGNING DIFFERENTVALUES
TO X PERMISSIBLE AS PER DOMAIN RESTRICTIONS IF ANY .
SINCE THERE ARE NO DOMAIN RESTRICTIONS ON X AS CONCLUDED ABOVE
W CAN TAKE ANY VALUES OF THE FORM
T[X1,X2,X3]=[(5x1 - x2 +x3);( -x1 +x2 +7x3);(2x1 - 4x2 -x3 )]
WHICH REPRESENTS THE CO-DOMAIN OF THE TRANSFORM.

                                                                                                  T I need to find the domain and codomain of the transformationsx----->w defined by theequations, and determine whether T is linear. If you could please help at all, please list the steps and/orexplain. Thanks so much!!
DOMAIN IS THE SET OF VALUES OF X WHICH MAKE THE TRANSFORM
OPERATION MATHEMATICALLY PERMISSIBLE.
SINCE ALL RELATIONAL EQNS OF TRANSFORMATION ARE LINEAR COMBINATIONSOF DIFFERENT REAL NUMBERS WHICH DO NOT INVOLVE ANY IN-PERMISSIBLEOPERATION
LIKE DIVISION BY ZERO ETC...
THE DOMAIN IS ALL REAL NUMBERS FOR X ..THAT IS X CAN TAKE ANY REALVALUE.
CO - DOMAIN IS ALL THOSE VALUES OF W WE GET BY ASSIGNING DIFFERENTVALUES
TO X PERMISSIBLE AS PER DOMAIN RESTRICTIONS IF ANY .
SINCE THERE ARE NO DOMAIN RESTRICTIONS ON X AS CONCLUDED ABOVE
W CAN TAKE ANY VALUES OF THE FORM
T[X1,X2,X3]=[(5x1 - x2 +x3);( -x1 +x2 +7x3);(2x1 - 4x2 -x3 )]
WHICH REPRESENTS THE CO-DOMAIN OF THE TRANSFORM.

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