Question

Describe the possible echelon forms of a nonzero 2 x 2 matrix.

Answer 1

The question discusses the shape and orientation of hydrogen's 2p orbitals (2px, 2py, 2pz), each having one nodal plane and differing phases of the electron wave function. A nodal plane is where the electron probability is zero.

Step-by-step explanation:

The question provided refers to the electron probability distribution of hydrogen's 2p orbitals, which can be categorized into three types based on their orientation: 2px, 2py, and 2pz orbitals. These orbitals possess a characteristic shape and each has a nodal plane where the electron density is zero. The 2pz orbital has its lobes along the z-axis with a nodal plane on the xy plane. The 2px and 2py orbitals are similar in shape but align along the x-axis and y-axis, respectively. It's important to note that the sign of the wave function's phase in these orbitals indicates the phase of the electron motion, not electrical charges. Additionally, the mention of metastable positions in a 2x2 matrix illustrates potential related information but seems out of context in a discussion of electron orbital shapes.

Answer 2

we approach the issue by taking note of that a 2 x 2 matrix can either have 1 0r 2 pivot columns. If the matrix has no pivot columns then every entry in the matrix must be zero.

-> if our matrix has two pivot columns then :
`\left(\begin{array}{rr}-&*&0&-\end{array}\right)`

-> if our matrix has one pivot column then we have a choice to make. If the first column is pivot column then:
`\left(\begin{array}{rr}-&*&0&0\end{array}\right)`

->otherwise, if the pivot column is the second column then:
`\left(\begin{array}{rr}0&-&0&0\end{array}\right)`