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Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question

Transcribed Image Text:1. True or False:
a) Every basis of R³ has 2 vectors
b)
The standard basis of P4, polynomials of degree less than or equal to 4, is
{1, x, x², x³, x4}
c)
The matrix equation Ax=b is consistent if and only if b is in the col(A), the
column space of A
d)
e)
-
f)
h)
-
The set {x € R² : 2+2 ≤ 1} is a vector subspace of R²
-
If T V
I
spaces V, W then
W is a linear transformation between finite dimensional vector
dim(V)= dim(N(T)) + dim(R(T))
A linear transformation is one to one if its nullspace contains 6 nonzero vectors.
Every n x n symmetric matrix is orthogonally diagonalizable.
An eigenvector is always nonzero.
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