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- Find the bases for the four fundamental subspaces of the matrix. A=[010030101].Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the subspace. a Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B. b Apply the Gram-Schmidt orthonormalization process to transform B into an orthonormal set B. c Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B.Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
- 1. Is the set of all 2 x 2 matrices of the form a 1/ 1 b , where a and b may be any scalars, a vector subspace of all 2 x 2 matrices?Is the set of noninvertible 2 × 2 matrices a subspace of R2×2 ?Let A be a 3 × 2 matrix with rank 2. Give geometric descriptions of R(A) and N(AT ), and describe geometrically how the subspaces are related.
- Let P2P2 be the vector space of all polynomials of degree 2 or less, and let HH be the subspace spanned by 4x2+11x−8, x2+4x−34x2+11x−8, x2+4x−3 and 4−5x4−5x. The dimension of the subspace HH is . Is {4x2+11x−8,x2+4x−3,4−5x}{4x2+11x−8,x2+4x−3,4−5x} a basis for P2P2? Be sure you can explain and justify your answer. A basis for the subspace HH is {{ }}. Enter a polynomial or a comma separated list of polynomials, where you can enter xx in place of x2x2.In R4 , find the dimension of the subspace spanned by the vectors {(1, 1, 1, 1)T , (1, 2, 2, 2)T , (1, 1, 2, 1)T , (2, 2, 3, 2)T , (4, 5, 6, 5)T }.In linear algebra, a subspace of R^n can have a dimension less than n. (True or False)