Math Snap

STEP 1

Assumptions1. We are given a linear transformation $(x)=Ax$ from $\mathbb{R}^{8}$ to $\mathbb{R}^{9}$.
. We need to find the dimensions of the matrix $A$ that defines this transformation.

STEP 2

In a linear transformation defined by a matrix multiplication, the number of columns in the matrix must equal the dimension of the input space. This is because each column of the matrix corresponds to a basis vector in the input space.
$$\text{Number of columns in } A = \text{Dimension of input space}$$

STEP 3

Substitute the given dimension of the input space into the equation.
$$\text{Number of columns in } A =8$$

STEP 4

Similarly, the number of rows in the matrix must equal the dimension of the output space. This is because each row of the matrix corresponds to a basis vector in the output space.
$$\text{Number of rows in } A = \text{Dimension of output space}$$

Substitute the given dimension of the output space into the equation.
$$\text{Number of rows in } A =9$$So, the matrix $A$ must have9 rows and8 columns. Therefore, the correct answer is B. The matrix A must have9 rows and8 columns.