Untitled Quiz

<p>Leftmost non-zero entry in a non-zero row</p> Signup and view all the answers

<ol> <li>All nonzero rows are above any all zero rows; 2. Each leading entry is in a column to the right of the previous leading entry; 3. All entries below a leading entry in its column are zeros</li> </ol> Signup and view all the answers

<p>Same as echelon form, except all leading entries are 1 and each leading 1 is the only non-zero entry in its row.</p> Signup and view all the answers

<p>The collection of all vectors in R^n that can be written as c1v1 + c2v2 +...</p> Signup and view all the answers

<p>Each b is a linear combination of A and has at least one solution for each b in R^n.</p> Signup and view all the answers

<p>A position in the original matrix that corresponds to a leading 1 in a reduced echelon matrix.</p> Signup and view all the answers

<p>A column that contains a pivot position.</p> Signup and view all the answers

<p>A system that can be written as Ax = 0.</p> Signup and view all the answers

<p>If only the trivial solution exists for a linear equation.</p> Signup and view all the answers

<p>If non-zero weights that satisfy the equation exist.</p> Signup and view all the answers

<p>Assigns each vector x in R^n a vector T(x) in R^m.</p> Signup and view all the answers

<ol> <li>AB != BA; 2. If AB = AC, B does not necessarily equal C; 3. If AB = 0, it cannot be concluded that either A or B is equal to 0.</li> </ol> Signup and view all the answers

<p>Flips rows and columns.</p> Signup and view all the answers

<ol> <li>(A^T)^T = A; 2. (A+B)^T = A^T + B^T; 3. (rA)^T = r<em>A^T; 4. (AB)^T = B^T</em>A^T.</li> </ol> Signup and view all the answers

<ol> <li>If A is invertible, (A^-1)^-1 = A; 2. (AB)^-1 = B^-1 * A^-1; 3. (A^T)^-1 = (A^-1)^T.</li> </ol> Signup and view all the answers

<p>A is invertible; A is row equivalent to I; A has n pivot columns; Ax = 0 has only the trivial solution; the transformation x --&gt; Ax is one to one; and more.</p> Signup and view all the answers

<p>col1Arow1B +...</p> Signup and view all the answers

<ol> <li>Ly = b; Ux = y; 2. Reduce A to echelon form; 3. Place values in L that would reduce it to I.</li> </ol> Signup and view all the answers

<p>x = Cx + d.</p> Signup and view all the answers

<ol> <li>The zero vector is in H; 2. For u and v in H, u + v is also in H; 3. For u in H, cu is also in H.</li> </ol> Signup and view all the answers

<p>Set of all the linear combinations of the columns of A.</p> Signup and view all the answers

<p>Set of all solutions to Ax = 0.</p> Signup and view all the answers

<p>A linearly independent set in H that spans H; the pivot columns of A form a basis for A's column space.</p> Signup and view all the answers

<p>The number of vectors in any basis of H; the zero subspace's dimension is 0.</p> Signup and view all the answers

<p>The dimension of the column space.</p> Signup and view all the answers

<p>A transformation that assigns a vector y in R^m for each x in R^n; there's a pivot in every column.</p> Signup and view all the answers

<p>Consistent for any b; pivots in all rows.</p> Signup and view all the answers

<p>A matrix product u^Tv or u.v where u and v are vectors.</p> Signup and view all the answers

<ol> <li>x is in W' if x is perpendicular to every vector that spans W; 2. W' is a subspace of R^n.</li> </ol> Signup and view all the answers

<p>A set of vectors where u_i.u_j = 0 (and i != j).</p> Signup and view all the answers

<p>An orthogonal set of unit vectors.</p> Signup and view all the answers