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 Nov7 asked Find a basis for the set of vectors in $\mathbb{R}^4$ in the subspace (hyperplane) $x_1 +x_2 + 2x_3 + x_4 = 0, x_1 + 2x_2-x_3=0$ Nov7 asked How can I prove a basis (for RowA, NulA, ColA, or NulA^T) with orthogonality conditions? Nov7 comment Give an example of a $3$-dimensional subspace of $P_4$ which contains the polynomials… This answer was fantastic, albeit a bit over my head. I believe this is an Einstein Summation? I'm assuming part of what it does can be labeled synonymous with the definition of linear independent if it = 0. I will study until I understand. Nov7 comment Give an example of a $3$-dimensional subspace of $P_4$ which contains the polynomials… No prob! Just making sure. I'm reading your solution now. Thank you so much for your insight. Nov7 comment Give an example of a $3$-dimensional subspace of $P_4$ which contains the polynomials… Just curious if I'm missing the obvious, but where does the + 4t^4 come from? Did you combine the first two polynomials? Nov7 comment Give an example of a $3$-dimensional subspace of $P_4$ which contains the polynomials… Ah, that's pretty straight forward. It was unclear to me. Is the fact that the subspace must be 3-dimensional significant to the answer, or would I just span the polynomials and/or prove that they are linearly (in)dependent? Nov7 comment Give an example of a $3$-dimensional subspace of $P_4$ which contains the polynomials… What exactly is P_4? Nov7 asked Give an example of a $3$-dimensional subspace of $P_4$ which contains the polynomials… Oct17 accepted Determinants of Variables Oct17 accepted Explain why a determinant function is a cubic polynomial Oct17 comment Explain why a determinant function is a cubic polynomial It doesn't say. That's all the book gives me. I assume it represents a square matrix. Oct17 asked Explain why a determinant function is a cubic polynomial Oct17 comment Need help with Determining a formula for a Resistance using a linear system for loop currents This is a fantastic answer. Oct17 comment Given a parallelepiped, how do I find the determinant given vertices? Great! Thank you Oct17 accepted Need help with Determining a formula for a Resistance using a linear system for loop currents Oct17 asked Given a parallelepiped, how do I find the determinant given vertices? Oct17 comment Determinants of Variables It would certainly alter the k value, but I'm not sure how to denote this. Oct17 comment Need help with Determining a formula for a Resistance using a linear system for loop currents Okay, great. And the equations you found are considered a "linear system" for the loop currents? Oct17 comment Determinants of Variables I'm not sure about the rows in the middle. That's all that is given. Oct17 comment Determinants of Variables The size isn't given.