Final answer:
The standard matrix of a linear transformation that performs a vertical shear, mapping e1 to e1 - 10e2 and leaving e2 unchanged, is a 2x2 matrix with columns [1, -10] and [0, 1].
Step-by-step explanation:
The question asks to find the standard matrix of a linear transformation t that maps the vector e1 into e1 - 10e2 while leaving e2 unchanged, which describes a vertical shear transformation. To find the standard matrix of t, we express the images of the standard basis vectors under t. Since t(e1) = e1 - 10e2, and t(e2) = e2, the standard matrix for t is a 2x2 matrix where the first column is the image of e1 and the second column is the image of e2. Therefore, the standard matrix A is:
A = [
10
-101
]
Where the first column represents t(e1) and the second column represents t(e2).