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In the space
a. Find
b. Find the norm of the constant function
c. Find
d. Find
e. Applying the Gram—Schmidt process to the standard basis
f. Find the polynomial
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Chapter 5 Solutions
Linear Algebra With Applications (classic Version)
- Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).arrow_forward5. Prove that the equation has no solution in an ordered integral domain.arrow_forwardIf x and y are elements of an ordered integral domain D, prove the following inequalities. a. x22xy+y20 b. x2+y2xy c. x2+y2xyarrow_forward
- Let f1(x)=3x and f2(x)=|x|. Graph both functions on the interval 2x2. Show that these functions are linearly dependent in the vector space C[0,1], but linearly independent in C[1,1].arrow_forwardUse the functions f and g in C[-1, 1] to find (f, g), f, g, and d(f, g) for the inner product (f, g) = f(x)g(x)dx. f(x) = 3x, g(x) = ex (a) (f, g) (b) ||f|| (c) ||g|| (d) d(f, g)arrow_forwardce #3 Consider p(x) = 3x - 2 and q (x) = x + 7. The evaluation inner product is defined as (p, q) = p (x1) a (x₁) +p (x₂) q (x₂)+p(x3) q (x3). For (1, 2, 3) = (1, -1, 3), what is the distance d (p, q)? O √179 C E 21 84 803 54 $ 4 DEC R G Search or type URL % 5 T MacBook Pro JAO A Y & 7 U * 00 8 + - ( 9 S ) 0 1 0 Parrow_forward
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