Download Calculus Quiz week 37.1 - Personal Web pages at the Department

University of Aarhus
Department of Mathematical Sciences
Calculus Quiz
week 37.1
Legend: A 4 indicates a correct response; a 8, indicates an incorrect response, in this case, the correct answer is marked with a l. Correct and follow
a 4,l for a solution. Return through n.
Fall 2004
2
Linear Equations
1. Which is not a row operation?
Interchancing of two rows
Addition of a row to a scalation
of another row
Multiplication of a row with the
scalar −1
Subtraction of one row from
another
2. If the product of matrices AB = I, then also BA = I.
Yes
No
3. The system of linear equations
x − y + z = 0, x + y = 0
has infinitely many solutions?
Yes
No
3
4.
Yes
1
1
−1 2
3 −2
=
3
−1 1
No
5. If the coefficient matrix of the system of equations Ax = b is invertible,
then the solution is
Ab
bA−1
6. A row operation on a matrix is:
A right multiplication on the matrix
A left multiplication on the matrix
A−1 b
Solutions to Quizzes
4
Solutions to Quizzes
Solution to Quiz:
Addition of second row to 0 scalation of the first row gives
1 0
0 0
∼
0 0
0 0
which is not a row operation.
Solutions to Quizzes
Solution to Quiz:
No, by [LA] Theorem 10 this is true only for square matrices.
5
Solutions to Quizzes
Solution to Quiz:
Yes, this is [LA] Theorem 9.
6
Solutions to Quizzes
7
Solution to Quiz:
Yes, Calculate
1 2
3 −2
1
=
1 3
−1 1
0
and conclude by [LA] Theorem 10.
0
1
Solutions to Quizzes
8
Solution to Quiz:
If Ax = b then
x = A−1 Ax = A−1 b
Solutions to Quizzes
9
Solution to Quiz:
[LA] Section 7: A row operation is a left multiplication on the matrix.