Question Video: Evaluating Expressions Involving the Addition and Scalar Multiplication of Given Vectors Mathematics

If 𝐀 = ⟨2, 3, 1⟩ and 𝐁 = ⟨1, 3, 2⟩, find 2𝐀 + 3𝐁.

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Video Transcript

If vector 𝐀 is equal to two, three, one and vector 𝐁 is equal to one, three, two, find two 𝐀 plus three 𝐁.

In this question, we begin by multiplying both of our vectors by a scalar. We recall that in order to do this, we multiply each of the individual components by the scalar. Two multiplied by two is equal to four, two multiplied by three is equal to six, and two multiplied by one is equal to two. The vector two 𝐀 is equal to four, six, two. We can repeat this process to calculate three multiplied by vector 𝐁. This gives us the vector three, nine, six.

The final step in this question is to find the sum of these two vectors. We need to add the vectors four, six, two and three, nine, six. We do this by adding their corresponding components. Four plus three is equal to seven, six plus nine is equal to 15, and finally two plus six is equal to eight. If vector 𝐀 is equal to two, three, one and vector 𝐁 is equal to one, three, two, then two 𝐀 plus three 𝐁 is equal to seven, 15, eight.

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