To solve this problem, let's first take a closer look at what it means to project a vector onto the x-axis. Essentially, the question is asking for a matrix that, when multiplied with a vector, eliminates the y-component of the vector and keeps only the x-component. This process allows one to "project" the vector onto the x-axis.
We are looking for a 2x2 matrix that will satisfy this condition. By considering how matrix multiplication works, one realizes that to obtain the vector (x,0), the matrix must be of the following form:
| P1, P2 | = | 1, 0 |
| P3, P4 | | 0, 0 |
Let's name it Matrix P.
Therefore, when we multiply any vector (x,y) by Matrix P, the result would be the vector (x, 0), achieving the effect of projecting the original vector onto the x-axis.
Now, the second part of the question asks whether Matrix P is invertible. A matrix is invertible (i.e., it has an inverse) if and only if its determinant is not zero. Recall that the determinant of a 2x2 matrix is calculated as follows:
determinant_P = (P1 * P4) - (P2 * P3)
Substituting the values of Matrix P into the formula, we find that:
determinant_P = (1 * 0) - (0 * 0) = 0
Since the determinant of Matrix P is zero, Matrix P is not invertible.
Therefore, the answer is:
P = |1 0|, No |0 0|