The right hand side of the equation is 〈11 , -16 , 6〉
The values of a and b are a = 3 , b = -2
Step-by-step explanation:
If n . <a , b> + m . <c , d> = < x , y>, then
∵ a ∙〈5 , -4 , 0〉 + b ∙ 〈2 , 2 , -3〉 = 〈11 , -16 , 6〉
- By using the rule above
∴ a(5) + b(2) = 11 ⇒ (1)
∴ a(-4) + b(2) = -16 ⇒ (2)
∴ a(0) + b(-3) = 6 ⇒ (3)
Use equation (3) to find the value of b
∵ a(0) + b(-3) = 6
∴ 0 - 3b = 6
∴ -3b = 6
- Divide both sides by -3
∴ b = -2
Substitute b in equation (1) or equation (2) to find a
∵ a(5) + b(-2) = 11
∴ 5a - 2b = 11
∵ b = 2
∴ 5a - 2(2) = 11
∴ 5a - 4 = 11
- Add 4 to both sides
∴ 5a = 15
- Divide both sides by 5
∴ a = 3
To check your answer substitute a and b in equation (2)
∵ a(-4) + b(2) = -16
∴ -4a + 2b = -16
∵ a = 3 , b = -2
∵ The left hand side is -4a + 2b = -4(3) + 2(-2) = -12 - 4 = -16
∵ The right hand side is -16
∴ L.H.S = R.H.S
∴ The values of a and b are 3 , -2
The values of a and b are a = 3 , b = -2
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