Linear Algebra Concepts Quiz

The vector equation $x_1v_1 + x_2v_2 +...+ x_rv_r = 0$ can only be solved by choosing $x_1 = x_2 =...= x_r = 0$, the trivial solution.

The vector equation $x_1v_1 + x_2v_2 +...+ x_rv_r = 0$ has infinitely many solutions for $x_1, x_2,..., x_r$.

<p>A square matrix A with infinitely many solutions $x$ to the equation $Ax = 0$.</p> Signup and view all the answers

<p>A square matrix A for which the only solution to the equation $Ax = 0$ is $x = 0$, the trivial solution.</p> Signup and view all the answers

<p>All of the above</p> Signup and view all the answers

<p>Using the elementary row operations to transform an augmented matrix into RREF (row reduced echelon form).</p> Signup and view all the answers

<p>An $m \times n$ system with the right side of the system of equations all being 0 ($Ax = 0$).</p> Signup and view all the answers

<p>An $m \times n$ system where the right side of the system of equations is not all 0s ($Ax = b$).</p> Signup and view all the answers

<p>A system of equations that has one solution or infinitely many solutions.</p> Signup and view all the answers

<p>A system of equations that has no solution.</p> Signup and view all the answers

<p>Two matrices are row equivalent if one can be transformed into the other through elementary row operations.</p> Signup and view all the answers

<p>A system of equations written as a matrix in the form $[A | b]$.</p> Signup and view all the answers

<p>The solution $x_1 = x_2 =...= x_n = 0$.</p> Signup and view all the answers

<p>A n-tuple which is a n x 1 matrix.</p> Signup and view all the answers

<p>A number with no direction.</p> Signup and view all the answers

<p>Denoted $||x||$, found with the distance formula: $||x|| = \sqrt{(x_1)^2 + (x_2)^2 +...+ (x_n)^2}$.</p> Signup and view all the answers

<p>Denoted $e_i$ (arrow), dimension of n x 1, where there is a 1 in the ith position.</p> Signup and view all the answers

<p>Reduced Row Echelon Form</p> Signup and view all the answers

<p>If a matrix $A = A^T$, compare values across the main diagonal of the matrix.</p> Signup and view all the answers

<p>Starts at the top left and ends at the bottom right.</p> Signup and view all the answers

<p>Denoted $A^T$, found by interchanging rows and columns of A.</p> Signup and view all the answers