Is the zero vector a linear combination of any nonempty set of vectors?
Question: Is the zero vector a linear combination of any nonempty set of vectors ? Justify. Is the set of all differential real valued functions defined on R...
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Is the span of X is X? Does every vector space have finite basis?
Question a: Is the span of \(\phi\) is \(\phi\) ? justify. The vectors \(u_1 = ( 2, -3 , 1) , u_2 = (1 , 4 , -2) , u_3 = (-8 , 12 , -4) , u_4 = ( 1 , 37 , -1...
Is the empty set a subspace of every vector space? Justify
Question:a. Is the empty set a subspace of every vector space ? Justify and let s = \({(a, b, (a + b):a, b \in R)}\) . Is a subspace of \(R^3\) under the us...
Does ax = bx imply a = b in any vector space?justify
Question: Does ax = bx imply a = b in any vector space? Justify. Let v = \({(a_1, a_2):a_1, a_2 \in f}\) where f is field. Define addition of elements of v c...
The Power of ‘Why not?’
Introduction What if I did this? What if I couldn’t do this? $$ (a + b)^2 = a^2 + 2ab + b^2 (a - b)^2 = a^2 - 2ab + b^2
The Power of ‘What if?’
Introduction What if I did this? What if I couldn’t do this?