Final answer:
The dot product of the vectors [[1],[-4],[3]] and [[-5],[2],[7]] is a scalar value of 8, obtained by multiplying corresponding elements of the vectors and summing the products.
Step-by-step explanation:
The dot product (or scalar product) of the two column vectors [[1],[-4],[3]] and [[-5],[2],[7]] is calculated by multiplying corresponding elements of each vector and then summing these products. For these vectors, it is calculated as follows:
(1 * -5) + (-4 * 2) + (3 * 7) = -5 - 8 + 21 = 8.
The result of this calculation is 8, which is a scalar value. This is consistent with the property that the dot product of two vectors results in a scalar.