Recent questions tagged linear-algebra

4 votes
1 answer
185
Consider the $n \times n$ matrix $M$ defined as follows:$$M=\left(\begin{array}{cccc}1 & 2 & \ldots & n \\n+1 & n+2 & \ldots & 2 n \\2 n+1 & 2 n+2 & \ldots & 3 n \\\vdots...
0 votes
0 answers
186
Use LU Decomposition method to solve the following system.$\left\{\begin{matrix} & x_{1} +x_{2}-x_{3} =1 \\ & x_{1} +2x_{2}-2x_{3} =0 \\ & -2x_{1} +x_{2}+x_{3} =1 \end{ma...
0 votes
0 answers
187
Solve the following system using Gauss elimination with partial pivoting.$\left\{\begin{matrix} &2x_{1}+x_{2}+x_{3}=10\\ & 3x_{1}+2x_{2}+3x_{3}=18 \\ & 5x_{1}+4x_{2}+2x_{...
0 votes
0 answers
191
What is the equation of the plane that contains point (-2, 4, 5) and the vector (7, 0, -6) is normal to the plane? And check if this plane intersects the y-axis.
0 votes
0 answers
192
Find equation of a line passes through the points = (0, 1, 2) and = (-1, 1, 1).
0 votes
0 answers
193
Question: How NullSpace of the matrix A and the uniqueness of the solution of Ax=b are related ??
1 votes
0 answers
195
Calculate the eigenvalues of matrix $M, M^{-1}, M^{2}$ and $M+2 I$ where\[M=\left[\begin{array}{cc}4 & 5 \\2 & -5\end{array}\right].\]
1 votes
1 answer
196
With no unique solution, solve for $n$ with the following system of equations$$\begin{array}{r}a+b+2 c=3 \\a+2 b+3 c=4 \\a+4 b+n c=6\end{array}$$
0 votes
1 answer
197
To justify the OPTION B they gave an example of 2*2 matrix. However we can see that row 2 is linearly dependent on row1. Even though the 2nd row looks non-zero it can be ...
0 votes
0 answers
198