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Magazine Problem 3
Solve the following system of equations using the substitution method. $$ \begin{array}{l} 5 w-z=14 \\ 2 w+3 z=26 \end{array} $$
Problem 3
Which of the following recursive relations are linear difference equations? Which are homogeneous linear difference equations? $$ x_{n+1}=-13 x_{n}+14 x_{n-1}+2 x_{n-2} $$
Problem 3
Multiply the matrix and the vector to determine if the vector is an eigenvector. If so, what is the eigenvalue? $$ \left[\begin{array}{ll} 3 & 2 \\ 0 & 4 \end{array}\right],\left[\begin{array}{l} 0 \\ 1 \end{array}\right] $$
Problem 4
Which of the following recursive relations are linear difference equations? Which are homogeneous linear difference equations? $$ x_{n+1}=2 x_{11}-x_{n-1}+2 $$
Problem 4
Multiply the matrix and the vector to determine if the vector is an eigenvector. If so, what is the eigenvalue? $$ \left[\begin{array}{rr} 5 & 0 \\ 3 & -2 \end{array}\right],\left[\begin{array}{l} 1 \\ 0 \end{array}\right] $$
Problem 4
Compute the inverse matrix. $$ \left[\begin{array}{rr} -1 & 0 \\ 0 & 2 \end{array}\right] $$
Problem 4
Solve the following system of equations using the substitution method. $$ \begin{aligned} -2 r-5 s=&-8 \\ 3 r+2 s=& 1 \end{aligned} $$
Problem 5
Multiply the matrix and the vector to determine if the vector is an eigenvector. If so, what is the eigenvalue? $$ \left[\begin{array}{rr} 5 & 0 \\ 3 & -2 \end{array}\right],\left[\begin{array}{l} 0 \\ 1 \end{array}\right] $$
Problem 5
Compute the inverse matrix. $$ \left[\begin{array}{ll} 3 & 4 \\ 5 & 7 \end{array}\right] $$
Problem 6
Multiply the matrix and the vector to determine if the vector is an eigenvector. If so, what is the eigenvalue? $$ \left[\begin{array}{rr} 10 & 0 \\ 42 & -4 \end{array}\right],\left[\begin{array}{l} 1 \\ 3 \end{array}\right] $$
