Final answer:
A standard matrix for a linear transformation from R^3 to R^2 is a 2x3 matrix that represents the transformation as a matrix multiplication.
Step-by-step explanation:
In linear algebra, a standard matrix represents a linear transformation by expressing the transformation as a matrix multiplication. If the linear transformation takes a vector from R^3 to R^2, the standard matrix will be a 2x3 matrix.
To find the standard matrix for the transformation, we need to determine where the standard basis vectors of R^3 are mapped to in R^2. Let's denote the standard basis vectors of R^3 as i, j, and k, and their images in R^2 as a and b, respectively. For example, if i is mapped to a, then a is the first column of the standard matrix.
Once we have determined the images of i, j, and k, we can write the standard matrix as:
[a, b]
where a and b are column vectors in R^2.