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Linear Algebra Algebra 1 Algebra 2 Algebra

07/20/21

𝑣=⟨7,3,10⟩ v = ⟨ 7 , 3 , 10 ⟩ 𝑤=⟨6,6,10⟩ w = ⟨ 6 , 6 , 10 ⟩ Find the cosine of the angle between 𝑣 v and 𝑤 w .

Find the cosine of the angle between and .

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Linear Algebra Algebra 1 Algebra 2 Algebra

07/20/21

) Given the vectors 𝑎=(1,2,3) a = ( 1 , 2 , 3 ) and 𝑏=(1,−1,2) b = ( 1 , − 1 , 2 ) , what is the dot product 𝑎⋅𝑏⋅𝑎 a ⋅ b ⋅ a ?

) Given the vectors and , what is the dot product ?

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Linear Algebra Algebra 1 Algebra 2 Algebra

07/20/21

Which of the following vectors is perpendicular to 𝑎=(1,2,3) a = ( 1 , 2 , 3 ) and 𝑏=(1,−1,2) b = ( 1 , − 1 , 2 ) ?

which of the following is perpendicualr to said vector

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Linear Algebra Algebra 1 Algebra 2 Algebra

07/20/21

Consider the vector 𝑣⎯⎯⎯ v ¯ between (−2,4,−5) ( − 2 , 4 , − 5 ) and (5,−2,−4) ( 5 , − 2 , − 4 ) .

the vector v ¯ is? THE LENGTH OF v ¯ IS? if the tail of v ¯ is at (5,-1,1), then the tip is at? if the tip of v ¯ is at (0, -5, -2) then the tail is at ? what vector has the same length as v ¯ but... more

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Linear Algebra Algebra

07/20/21

Find 𝐚⋅𝐛 a ⋅ b if |𝐚|=6 | a | = 6 , |𝐛|=1 | b | = 1 , and the angle between 𝐚 a and 𝐛 b is 𝜋/4 π / 4 .

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Linear Algebra Maths

07/20/21

Suppose T: R² → R² is a linear operator with T ([1,2]) = [1, 1] and T ([2,0]) = [2, −4].

Give a formula T([x, y]) for any[x, y] ∈ R² . Also find a basis for ker(T), a basis for range(T) and verify the dimension theorem

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Linear Algebra Maths

07/20/21

For the subspace W = {[x, y, z] ∈ R³ ∶ 2x − 2y + z = 0} of R³,

find a basis for the orthogonal complement W‘ and verify that dim(W) + dim(𝑊') = dim(R³ ) Decompose v = [1, 2, 3] into w1 + w2, where 𝑤1 ∈ W and 𝑤2∈ 𝑊'

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Linear Algebra Maths

07/20/21

Find the minimum distance between the given point P and the given subspace W of R³, P = (4, −1, 2), W = span({[−2, 3, −3]}) in R³

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Linear Algebra Linear Equations

07/18/21

how to write this in point-slope intercept form? Slope=-2 and point=(1,-1)

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Linear Algebra

07/18/21

how to write this in point-slope intercept form? Slope=-6/5 and Y-intercept=2.

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Linear Algebra Slope Intercept Form

07/18/21

How to write point one=(0,-2) and point two=(-3,-5) in slope-intercept form?

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Linear Algebra Slope Intercept Form

07/18/21

Slope=-4 and Point=(2,-4) how to write it in slope-intercept form?

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Linear Algebra Slope Intercept Form

07/18/21

Slope=-4 and Point=(2,-4) how to write it in slope-intercept form?

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Linear Algebra

07/18/21

linear combination of the basis vectors

Consider the set of vectors in R3 given by a1=(1, 0, 0), a2=(1,-2,0), a3=(0,0,1).Write the vector x=(1, 2, 5) as a linear combination of the basis vectors a1, a2, a3.

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Linear Algebra Algebra

07/16/21