D. Linear combination Note that [14 - 3 of vectors: 2 ][59] [5.1 + 9.4 5.3 + 9₁ -2] = 5[13]+9[42]. 1. Let v₁ = [₁₁₁2] et v₁ = [2122] be two column vectors. Express the linear combination C₁v₁ + c₂v₂ as a matrix multiplication. 2. Let 1 .....be MX1 column vectors, and let = be a column vector of size 1xN. Write the linear combination cv +... N as a matrix multiplication. 5. Let ... be row vectors of size 1XN, and let c'be a row vector of size 1xM. Write the M combination + ...c vas a matrix multiplication. MM

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Chapter6: Linear Transformations
Section6.4: Transistion Matrices And Similarity
Problem 13E
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Please do Question D part 1,2, and 5. Please show step by step and explain. Please take note of the Notations

D. Linear combination of vectors:
Note that [1432 ][59] [5.1 + 9.4 5.3+ 9. 2] = 5[1-3]+9[42].
1. Let V₁ = [V₁₁ V₁2 ] et ₁₂ = [V2₁22] be two column vectors. Express the linear combination
11
cv as a matrix multiplication.
....,vbe Mx1 column vectors, and let c = be a column vector of size 1xN. Write the
N
2. Let v
linear combination cv₁ +...c as a matrix multiplication.
N N
5. Let v
,vbe row vectors of size 1xN, and let c be a row vector of size 1xM. Write the
combination cv + ...vas a matrix multiplication.
MM
Notation: If ,... are column vectors, then the matrix whose j'th column is a can be written as
M
[...].
Transcribed Image Text:D. Linear combination of vectors: Note that [1432 ][59] [5.1 + 9.4 5.3+ 9. 2] = 5[1-3]+9[42]. 1. Let V₁ = [V₁₁ V₁2 ] et ₁₂ = [V2₁22] be two column vectors. Express the linear combination 11 cv as a matrix multiplication. ....,vbe Mx1 column vectors, and let c = be a column vector of size 1xN. Write the N 2. Let v linear combination cv₁ +...c as a matrix multiplication. N N 5. Let v ,vbe row vectors of size 1xN, and let c be a row vector of size 1xM. Write the combination cv + ...vas a matrix multiplication. MM Notation: If ,... are column vectors, then the matrix whose j'th column is a can be written as M [...].
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