Answer:
(c) [-10 10 -30]
Step-by-step explanation:
Apparently, you're multiplying a vector by a scalar. The product is the vector that results from multiplying each term by the scalar (5). That is, the product is ...
[5(-2) 5(2) 5(-6)] = [-10 10 -30]
For this purpose, the brackets can be treated in much the same way as the parentheses used in the distributive property.
_____
Additional comments
You will see different kinds of vector notation. This is one that my HP-48 calculator uses. My TI-84 calculator uses commas to separate elements in the vector: [-10,10,-30]. This vector would be considered to be a row vector. In most cases, if you want your calculator to recognize it as a column vector, you must put each element in its own row: [[-10] [10] [-30]].
__
Addition and subtraction of vectors and matrices work on an element-by-element basis.
Multiplication can be by a scalar (as here), or by another vector or matrix. There are specific form factors that must be observed when multiplying two vectors or matrices: the number of columns in the first one must equal the number of rows in the second one.
Additional multiplication-type operations can be performed on two vectors: "dot" product, and "cross" product. These, too, have specific definitions different from the scalar multiplication in this problem.
__
Most spreadsheets can perform vector and matrix operations, as can most graphing calculators. It can be worthwhile to learn to use one of these tools.
