Indicate whether statement is true or not. Justify answer withexample or theorem

Question

Indicate whether statement is true or not. Justify answer withexample or theorem. a)If x+y=x+z, theny=x b)If u+v=0 then u+bv=0 for all and b values c)Parallel vectors with the same length are equal d)If x=0 then either =0 or x=0 e)If u+bv=0 then u and v are parallel vectors f)The vectors u=(2, 3) and v=((1/2),.53) ARE EQUIVALENT Thanks! Indicate whether statement is true or not. Justify answer withexample or theorem. a)If x+y=x+z, theny=x b)If u+v=0 then u+bv=0 for all and b values c)Parallel vectors with the same length are equal d)If x=0 then either =0 or x=0 e)If u+bv=0 then u and v are parallel vectors f)The vectors u=(2, 3) and v=((1/2),.53) ARE EQUIVALENT Thanks! b)If u+v=0 then u+bv=0 for all and b values c)Parallel vectors with the same length are equal d)If x=0 then either =0 or x=0 e)If u+bv=0 then u and v are parallel vectors f)The vectors u=(2, 3) and v=((1/2),.53) ARE EQUIVALENT Thanks!

Explanation / Answer

QuestionDetails: Indicate whether statement is true or not. Justify answer withexample or theorem. a)If x+y=x+z, theny=x
TRUE
-X+X+Y=-X+X+Z
0+Y=0+Z
Y=Z
b)If u+v=0 then u+bv=0 for all and b values
FALSE .....
LET U=[2,3] AND V=[-2,-3]
U+V=[2-2,3-3]=[0,0]
LET A=2;B=5
AU+BV=[4,6]+[-10,-15]=[-6,-9]...NOT ZERO

c)Parallel vectors with the same length are equal
TRUE IF THEY ARE HAVING SAME SENSE.IF THEY ARE HAVING OPPOSITESENSE FALSE.
IF U AND V ARE || VECTORS AND EQUAL IN LENGTH , THEN U=V OR U=-VDEPENDING ON
WHETHER ARE IN SAME DIRECTION OR OPPOSITE DIRECTIONS
d)If x=0 then either =0 or x=0
TRUE . SINCE THERE ARE NO ZERO DIVISORS IN SCALAR MULTIPLICATION OFVECTORS.,
e)If u+bv=0 then u and v are parallel vectors
TRUE
SINCE
AU = -BV
U= [-B/A]V = KV....WHERE K IS A SCALAR.
THAT IS
U||V
f)The vectors u=(2, 3) and v=((1/2), 1/2,3)
WHAT?? TYPO?? CHECK...TYPE WHAT YOU WANT CORRECTLY.
Thanks! b)If u+v=0 then u+bv=0 for all and b values
FALSE .....
LET U=[2,3] AND V=[-2,-3]
U+V=[2-2,3-3]=[0,0]
LET A=2;B=5
AU+BV=[4,6]+[-10,-15]=[-6,-9]...NOT ZERO

c)Parallel vectors with the same length are equal
TRUE IF THEY ARE HAVING SAME SENSE.IF THEY ARE HAVING OPPOSITESENSE FALSE.
IF U AND V ARE || VECTORS AND EQUAL IN LENGTH , THEN U=V OR U=-VDEPENDING ON
WHETHER ARE IN SAME DIRECTION OR OPPOSITE DIRECTIONS
d)If x=0 then either =0 or x=0
TRUE . SINCE THERE ARE NO ZERO DIVISORS IN SCALAR MULTIPLICATION OFVECTORS.,
e)If u+bv=0 then u and v are parallel vectors
TRUE
SINCE
AU = -BV
U= [-B/A]V = KV....WHERE K IS A SCALAR.
THAT IS
U||V
f)The vectors u=(2, 3) and v=((1/2), 1/2,3)
WHAT?? TYPO?? CHECK...TYPE WHAT YOU WANT CORRECTLY.
Thanks!

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