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Placement Test Practice — Linear Algebra
Placement Test Practice — Linear Algebra
Practice Test — 18 Questions
1. Add two $2 \times 2$ matrices entry-wise.
2. State the size of a $4 \times 1$ matrix.
3. Solve $x+y=4$, $x-y=0$.
4. Interpret a row $[0\;0\;|\;6]$.
5. Find $$\det\begin{bmatrix}1&2\3&5\end{bmatrix}.$$
6. Is a matrix with determinant $0$ invertible?
7. Find the magnitude of $\langle 5,12 \rangle$.
8. Compute $\langle 1,0 \rangle\cdot\langle 0,7 \rangle$.
9. What does dot product $0$ tell you?
10. Multiply $$\begin{bmatrix}1&1\0&2\end{bmatrix}\begin{bmatrix}3\4\end{bmatrix}.$$
11. What is the determinant of $$\begin{bmatrix}2&0\0&2\end{bmatrix}$$?
12. What is the determinant of the identity matrix?
13. Add $\langle 2,3 \rangle + \langle -1,8 \rangle$.
14. Solve $2x+y=8$, $x-y=1$.
15. State one elementary row operation.
16. When is matrix multiplication defined?
17. Why are inverses useful?
18. What object stores the coefficients of a system compactly?
Show Answer Key
1. Matching entries are added.
2. 4 rows, 1 column
3. $(2,2)$
4. No solution
5. $-1$
6. No
7. $13$
8. $0$
9. Perpendicular vectors
10. $$\begin{bmatrix}7\8\end{bmatrix}$$
11. $4$
12. $1$
13. $\langle 1,11 \rangle$
14. $(3,2)$
15. Swap rows; scale a row; add a multiple of one row to another
16. Inner dimensions must match
17. They solve systems and undo linear transformations
18. A coefficient or augmented matrix