Question

For what value of m, the vector (m,3,1) is a linear combination of the vectors (3,2,1) and (2,1,0)?

Answer 1

SOLUTION

TO DETERMINE

The value of m for which the vector (m,3,1) is a linear combination of the vectors (3,2,1) and (2,1,0)

EVALUATION

Here it is given that vector (m,3,1) is a linear combination of the vectors (3,2,1) and (2,1,0)

So there exists two non zero scalers a and b such that

(m,3, 1) = a(3,2,1) + b(2,1,0)

⇒ (m,3, 1) = ( 3a + 2b, 2a + b , a )

Comparing both sides we get

3a + 2b = m

2a + b = 3

a = 1

From above we get

a = 1 , b = 1

Consequently m = 3a + 2b = 5

FINAL ANSWER

Hence the required value of m = 5

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Answer 2

Step-by-step explanation:

(m,3, 1) = a(3,2,1) + b(2,1,0)

=(m,3, 1) = ( 3a + 2b, 2a + b , a )

we get

3a + 2b = m

2a + b = 3

a = 1

From above we get

a = 1 , b = 1

Consequently m = 3a + 2b = 5

Answer =value of m = 5