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assume u4 is not a linear combination of {u1,u2,u3}

Select the best statement.

A. {u1,u2,u3,u4} is a linearly independent set of vectors unless one of {u1,u2,u3} is the zero vector.
B. {u1,u2,u3,u4}could be a linearly independent or linearly dependent set of vectors depending on the vector space chosen.
C. {u1,u2,u3,u4}is always a linearly dependent set of vectors.
D. {u1,u2,u3,u4} is never a linearly dependent set of vectors.
E. {u1,u2,u3,u4}is a linearly dependent set precisely when {u1,u2,u3} is a linearly dependent set.
F. none of the above

Respuesta :

Answer:

A. {u1,u2,u3,u4} is a linearly independent set of vectors unless one of {u1,u2,u3} is the zero vector.

Step-by-step explanation:

Given that u4 is not a linear combination of {u1,u2,u3}

This means there is no possibility to write u4 = au1+bu2+cu3 for three scalars a,b,and c.

This gives that [tex]u_4-au_1-bu_2-cu_3 \neq 0[/tex]

This implies that these four vectors are not linearly dependent but linearly independent.

Hence option a is right.

A. {u1,u2,u3,u4} is a linearly independent set of vectors unless one of {u1,u2,u3} is the zero vector.

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