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 Nov 19 comment Describe the smallest subspace of $M_{2\times 2}$ that contains matrices… @BrianM.Scott, how does this translate to a basis? I'm used to row reducing into free variables that I translate into a general solution. Nov 19 comment Describe the smallest subspace of $M_{2\times 2}$ that contains matrices… I guess my first instinct is to think, "No solution!". So if it's fine, then how do I translate that to a basis? Is it a free variable column, and I just disregard the column of 0s before it? Nov 19 comment Describe the smallest subspace of $M_{2\times 2}$ that contains matrices… I actually did that, though I got [1 0 0 2; 0 1 0 -4; 0 0 0 -4]. I'm not sure what to make of the last row. Do I just disregard it? Nov 19 asked Describe the smallest subspace of $M_{2\times 2}$ that contains matrices… Nov 19 asked Let $M_{2\times 2}$ be the vector space of all $2\times 2$ matrices. Show that the set of non-singular matrices is NOT a subspace. Nov 12 accepted Let $B =${$1-t^2, t-t^2, 2-2t+t^2$}. Check that $B$ is a basis for $P_2$ and find $[3+t-6t^2]_B$ Nov 12 accepted How can I prove a basis (for RowA, NulA, ColA, or NulA^T) with orthogonality conditions? Nov 7 comment How can I prove a basis (for RowA, NulA, ColA, or NulA^T) with orthogonality conditions? The edition is the 4th Nov 7 comment How can I prove a basis (for RowA, NulA, ColA, or NulA^T) with orthogonality conditions? Linear Algebra by David C Lay, Chapter 4 Nov 7 accepted Give an example of a $3$-dimensional subspace of $P_4$ which contains the polynomials… Nov 7 comment How can I prove a basis (for RowA, NulA, ColA, or NulA^T) with orthogonality conditions? Ok. I'll have to figure how to extract the SVD from A. Nov 7 accepted 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 comment Let $B =${$1-t^2, t-t^2, 2-2t+t^2$}. Check that $B$ is a basis for $P_2$ and find $[3+t-6t^2]_B$ Okay. So, how would I find this from B? How would I prove that B is the basis for P_2? I'm not sure where to start. Nov 7 comment How can I prove a basis (for RowA, NulA, ColA, or NulA^T) with orthogonality conditions? @LittleO, how so? Nov 7 asked Let $B =${$1-t^2, t-t^2, 2-2t+t^2$}. Check that $B$ is a basis for $P_2$ and find $[3+t-6t^2]_B$ Nov 7 comment Find a basis for the set of vectors in $\mathbb{R}^4$ in the subspace (hyperplane) $x_1 +x_2 + 2x_3 + x_4 = 0, x_1 + 2x_2-x_3=0$ A sheet my professor gave out as practice problems for our test. 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