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a. span\(V_1, V_2, ..., V_n\) = V means that any vector v ? V can be expressed b. The vectors V_1, V_2,..., V_n are linear independent when C_1V_1 + C_2V_2+...+C_nV_n = 0 has ________ solution, namely (C_1, C_2,..., C_n) = ________. c. To say that B = \{V_1, V_2, ..., V_n\} forms a basis for V means that and . d. If B = \{V_1, V_2, ..., V_n\} is a basis for V then any vector v ? V can be expressed as a linear combination of the vectors in B. e. If B = \{V_1, V_2, ..., V_n\} is a basis for V, and v ? V, then [v]_B = (C_1, C_2, ..., C_n) means that ______. f. To say that B = \{u_1, u_2, ..., u_n\} is an orthogonal basis of V means that ______. g. To say that B = \{w_1, w_2, ..., w_n\} is an orthonormal basis of V means that . h. Orthogonal (and orthonormal) bases are useful because .

          a. span\(V_1, V_2, ..., V_n\) = V means that any vector v ? V can be expressed
b. The vectors V_1, V_2,..., V_n are linear independent when
C_1V_1 + C_2V_2+...+C_nV_n = 0 has ________ solution, namely
(C_1, C_2,..., C_n) = ________.
c. To say that B = \{V_1, V_2, ..., V_n\} forms a basis for V means that ______ and ______.
d. If B = \{V_1, V_2, ..., V_n\} is a basis for V then any vector v ? V can be expressed
as a linear combination of the vectors in B.
e. If B = \{V_1, V_2, ..., V_n\} is a basis for V, and v ? V, then [v]_B = (C_1, C_2, ..., C_n)
means that ______.
f. To say that B = \{u_1, u_2, ..., u_n\} is an orthogonal basis of V means that ______.
g. To say that B = \{w_1, w_2, ..., w_n\} is an orthonormal basis of V means that ______.
h. Orthogonal (and orthonormal) bases are useful because ______.

a. spanV1, V2, ..., Vn = V means that any vector v ? V can be expressed
b. The vectors V1, V2,..., Vn are linear independent when
C1V1 + C2V2+...+CnVn = 0 has solution, namely
(C1, C2,..., Cn) = .
c. To say that B = {V1, V2, ..., Vn} forms a basis for V means that and .
d. If B = {V1, V2, ..., Vn} is a basis for V then any vector v ? V can be expressed
as a linear combination of the vectors in B.
e. If B = {V1, V2, ..., Vn} is a basis for V, and v ? V, then [v]B = (C1, C2, ..., Cn)
means that .
f. To say that B = {u1, u2, ..., un} is an orthogonal basis of V means that .
g. To say that B = {w1, w2, ..., wn} is an orthonormal basis of V means that .
h. Orthogonal (and orthonormal) bases are useful because .

Added by Lisa A.

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