A sum of scalar multiples of two or more vectors (such as c 1 Bold u plus c 2 Bold v plus c 3 Bold wc1u+c2v+c3w , where c Subscript ici are scalars) is called a linear combination of the vectors. Let iequals=left angle 1 comma 0 right angle1,0 and jequals=left angle 0 comma 1 right angle0,1. Express left angle negative 4 comma 9 right angle-4,9 as a linear combination of i and j (that is, find scalars c 1c1 and c 2c2 such that left angle negative 4 comma 9 right angle-4,9equals=c 1c1iplus+c 2c2j ).

Question

Tommy Schneider

Mathematics

31 August, 14:11

A sum of scalar multiples of two or more vectors (such as c 1 Bold u plus c 2 Bold v plus c 3 Bold wc1u+c2v+c3w , where c Subscript ici are scalars) is called a linear combination of the vectors. Let iequals=left angle 1 comma 0 right angle1,0 and jequals=left angle 0 comma 1 right angle0,1. Express left angle negative 4 comma 9 right angle-4,9 as a linear combination of i and j (that is, find scalars c 1c1 and c 2c2 such that left angle negative 4 comma 9 right angle-4,9equals=c 1c1iplus+c 2c2j ).

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Answers (1)

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Grayson Stewart · Answer 1

-4+9=

Step-by-step explanation:

i=

j=

We are required to find scalar multiples c₁ and c₂ such that

c₁i+c₂j=

c₁+c₂=

+<0, c₂>=

This implies that

c₁+0=-4

c₁=-4

0+c₂=9

c₂=9

Since we have found the values of the scalar multiples c₁ and c₂, we next express as a linear combination of i and j.

This is given as:

-4+9=