choice questions
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This activity contains 10 questions.
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false
If
false
which of the following is false?
If A and B are n × n matrices, which of the following does not equal (A
+ B)2?
(B + A)2
(A + B)A + (A + B)B
A2 + AB + BA + B2
A2 + 2AB + B2
If A, B, and C are n × n matrices, which of the following equalities is
invalid? Note: D′ is the transpose of D.
((AB)2)′ = (B′)2(A′)2
(ABC)′ = C′B′A′
(A + A)′ = 2A′
(A + A + 2B)′ = 2B′ + 2A′
The n × n matrix P is idempotent if P2 = P and orthogonal if P′P = I.
Which of the following is false?
If P is idempotent, then −P is idempotent
is orthogonal
If P and Q are idempotent n × n matrices and PQ = QP = O, then P + Q is
idempotent
If P and Q are orthogonal n × n matrices, then PQ is orthogonal
Which of the following statements is correct?
It is possible to construct a linear system with exactly 5 different solutions
A linear system can only have an infinite number of solutions if there are more
variables than equations
A linear system with more equations than unknowns cannot have solutions
Suppose A is n × n, x is n × 1, and Ax = 0 has only the trivial solution. Then Ax
= b has solutions for any n × 1 vector b
For which values of t does the following linear equation system have
infinitely many solutions?
t = −3
t=2
t = 2 and t = −3
The system does not have infinitely many solutions for any value of t
Using Gaussian elimination, the solutions of:
can be deduced from the augmented matrix
For which values of a, b, and c are there infinitely many solutions?
If c = 1
Never
If a = b and c = 1
If a ≠ b
If a = (3, 4, 0) and b = (0, 2, −3), then
is equal to:
3
0
2
−3
The straight line in
through the point (−1, 3, 3) pointing in the
direction of the vector (1, 2, 3) hits the x1x2-plane at the point:
(−2, 1, 0)
(2, −1, 0)
Never
(1, 3, 0)
The plane in
through the point (−1, 3, 3), which is orthogonal to the
vector (1, 2, 3), has the equation:
−x + 3y + 3z = 14
x − 2y − 3z = −16
x + 2y + 3z = 11
x + 2y + 3z = 14