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 Nov 7 comment Find a basis for the set of vectors in $\mathbb{R}^4$ in the subspace (hyperplane) $x_1 +x_2 + 2x_3 + x_4 = 0, x_1 + 2x_2-x_3=0$ The actual problem itself says that in the question. Nov 7 revised Find a basis for the set of vectors in $\mathbb{R}^4$ in the subspace (hyperplane) $x_1 +x_2 + 2x_3 + x_4 = 0, x_1 + 2x_2-x_3=0$ added 223 characters in body Nov 7 comment Find a basis for the set of vectors in $\mathbb{R}^4$ in the subspace (hyperplane) $x_1 +x_2 + 2x_3 + x_4 = 0, x_1 + 2x_2-x_3=0$ It might not be, I could be wrong. I just followed a heuristic I found online, since it doesn't seem to be in my textbook. Nov 7 revised How can I prove a basis (for RowA, NulA, ColA, or NulA^T) with orthogonality conditions? added 41 characters in body Nov 7 comment How can I prove a basis (for RowA, NulA, ColA, or NulA^T) with orthogonality conditions? Revised! Sorry about that. I should note that the question I'm reading isn't clear on what orthogonality conditions are, and that is where I'm confused. Thank you for the formatting advice. Nov 7 revised Find a basis for the set of vectors in $\mathbb{R}^4$ in the subspace (hyperplane) $x_1 +x_2 + 2x_3 + x_4 = 0, x_1 + 2x_2-x_3=0$ added 33 characters in body Nov 7 revised How can I prove a basis (for RowA, NulA, ColA, or NulA^T) with orthogonality conditions? added 621 characters in body Nov 7 asked Find a basis for the set of vectors in $\mathbb{R}^4$ in the subspace (hyperplane) $x_1 +x_2 + 2x_3 + x_4 = 0, x_1 + 2x_2-x_3=0$ Nov 7 asked How can I prove a basis (for RowA, NulA, ColA, or NulA^T) with orthogonality conditions? Nov 7 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. Nov 7 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. Nov 7 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? Nov 7 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? Nov 7 comment Give an example of a $3$-dimensional subspace of $P_4$ which contains the polynomials… What exactly is P_4? Nov 7 asked Give an example of a $3$-dimensional subspace of $P_4$ which contains the polynomials… Oct 17 accepted Determinants of Variables Oct 17 accepted Explain why a determinant function is a cubic polynomial Oct 17 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. Oct 17 asked Explain why a determinant function is a cubic polynomial Oct 17 comment Need help with Determining a formula for a Resistance using a linear system for loop currents This is a fantastic answer.