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Given the matrix 𝐴 which has elements eight, negative three, one, negative two, what is two 𝐴?
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In this question, we’re being asked to take the matrix 𝐴 and multiply it by the value two, which is just a scalar.
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We recall then that, to multiply a matrix by a scalar, we just need to multiply each individual element in our matrix by that scalar.
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Let’s see what that looks like.
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Two 𝐴 then will be equal to two multiplied by the matrix with elements eight, negative three, one, negative two.
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Multiplying each element of this matrix 𝐴 individually by two will give the matrix with elements two times eight, two times negative three, two times one, and two times negative two.
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Two times eight is 16.
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Two times negative three is negative six.
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Two times one is two.
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And two times negative two is negative four.
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Two 𝐴 then is the two-by-two matrix with elements 16, negative six, two, negative four.