Question

Express a=i+9j-3k as a linear combination of b=3i+4j+2k and c=5i-j+7k and interpret the result

Answer 1

Answer:

Answer

−

i

−3

j

+4

k

=x(2

i

+

j

−4

k

)+y(2

i

−

j

+3

k

)+z(3

i

+

j

−2

k

)

−

i

−3

j

+4

k

=(2x+2y+3z)

i

+(x−y+z)

j

+(−4x+3y−z)

k

2x+2y+3z=−1

x−y+z=−3

−4x+3y−2z=4

2x+2y+3z=−1

2x−2y+2z=−6

3x−3y+3z=−9

−4x+3y−2z=4

4x+5z=−7−x+z=−5

x−z=5

4x+5z=−7

4x−4z=20

9z=−27

z=−3

x=24+2y−9=−1

y=2

−

i

−3

j

+4

k

=2(2

i

+

j

−4

k

)+2(2

i

−

j

+3

k

)−3(3

i

+

j

−2

k

)

Step-by-step explanation:

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