Determine if left{ begin{bmatrix}2 -4 1 end{bmatrix},begin{bmatrix}-3 5 -1 end{bmatrix} right} is a basis for Col begin{bmatrix}1 -3 1 end{bmatrix},begin{bmatrix}-3 7 -2 end{bmatrix}

Dolly Robinson 2021-02-25 Answered
Determine if {[241],[351]} is a basis for
Col[131],[372]
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Expert Answer

BleabyinfibiaG
Answered 2021-02-26 Author has 118 answers

{[241],[351]}

Since  any C in R such that [+241],[351]

So [241],[351]

are linearly independent.

Now for [131],=C1[241]+C2[351]2C13C2=1(1)4C1+5C2=3(2)C1C2=1(3)

From (3) C1=C2+1,

From (1) 2C2+23C2=1C2=1C2=1

Thus C1=2

So [131]=2[241]+(1)x[351]

Against for [372]=x[211]+y[351]2x3y=3(4)4x+5y=+7(5)xy=2(6)

From (6) x=y2

From (4) 2y43y=3y=1y=1
x=12=3

From (5) 4x(3)+5(1)=125=7

So [372]=(3)[211]+(1)[351]

So {[241],[351]}

generate col[133712] .

So {[241],[351]}

forms a basis of

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