In Exercises 7–10, show that { u 1 , u 2 } or { u 1 , u 2 , u 3 } is an orthogonal basis for ℝ 2 or ℝ 3 , respectively Then express x as a linear combination of the u ’s. 9. u 1 = [ 1 0 1 ] , u 2 = [ − 1 4 1 ] , u 3 = [ 2 1 − 2 ] and x = [ 8 − 4 − 3 ]
In Exercises 7–10, show that { u 1 , u 2 } or { u 1 , u 2 , u 3 } is an orthogonal basis for ℝ 2 or ℝ 3 , respectively Then express x as a linear combination of the u ’s. 9. u 1 = [ 1 0 1 ] , u 2 = [ − 1 4 1 ] , u 3 = [ 2 1 − 2 ] and x = [ 8 − 4 − 3 ]
In Exercises 7–10, show that {u1, u2} or {u1, u2, u3} is an orthogonal basis for ℝ2 or ℝ3, respectively Then express x as a linear combination of the u’s.
Show that B = {x,x³ + 2x² + 4, x² + 2, 1} is a basis for P3.
8. Show that {u1, u2}, {u1,u2, u3} is an orthogonal basis for R? or R°, respectively.
Then express x as a linear combination of the u's.
2
(a) u1 =
,U2
and x
-3
3
2
1
(b) u1
-3,u2
1 and x =
-3
U3
%3D
4
1
In Exercises 8–19, calculate the determinant of the given
matrix. Use Theorem 3 to state whether the matrix is
singular or nonsingular
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