3-5? seven
- 1-3? seven
(2)
6? five
-4-7
(3)
- 1/2 1/2 1/2
1/2? - 1/2 1/2
1/2 1/2? - 1/2
(4) 1/2
(5)A^3？ =?
0? 4-4
0? 0? 0
0? 8-8
2.？ (1)lamda is not convenient to input, so it is changed to K.
[? k，？ 1,? 1]
[? 1,? k，？ 1]
[? 1,? 1,? k]
Add everything to the first column.
[? k？ +? 2,? 1,? 1]
[? k？ +? 2,? k，？ 1]
[? k？ +? 2,? 1,? k]
R2-r 1； ? r3-r 1
[? k？ +? 2,? 1,? 1]
[? 0,? k？ -? 1,? 0]
[? 0,? 0,? k？ -? 1]
If a system of equations has a nonzero solution, there must be R(A)? & lt？ n
So? k？ =? 1
(2)
[? t，？ 2]
[? 1,? t？ +? 1]
[? 1,? 1]
Exchange line 1, 3
[? 1,? 1]
[? 1,? t？ +? 1]
[? t，？ 2]
R2-r 1； ? r3-t*r 1
[? 1,? 1]
[? 0,? t]
[? 0,? 2? -? t]
If a system of equations has a nonzero solution, there must be R(A)? & lt？ n
So there is no solution, that is, t takes any real number, and the equations cannot have non-zero solutions.
3.？ The product of (1) vectors? I don't understand. Did you copy the wrong question?
(2)
[? 1,? 1,? 2]
[? 1,? 2,? 3]
[? 0,? 1,? t]
r2？ -? r 1
[? 1,? 1,? 2]
[? 0,? 1,? 1]
[? 0,? 1,? t]
r3？ -? r2
[? 1,? 1,? 2]
[? 0,? 1,? 1]
[? 0,? 0,? t？ -? 1]
Then when? t？ =? 1? Time, linear correlation
(3)
Answer? =
1? 1? 0? 1
2? 3? 1? 2
0? 1? 1? 0
r2？ -? 2r 1
Answer? =
1? 1? 0? 1
0? 1? 1? 0
0? 1? 1? 0
r3？ -? r2
Answer? =
1? 1? 0? 1
0? 1? 1? 0
0? 0? 0? 0
So r(A)? =? 2
(4)r(A)？ =? 2r(B)？ =? three
R(AB)≤min(R(A)，？ R(B))=2
A is mxn? B is it? nxs？ Matrix? Yes? r(A)+r(B)-n & lt； =r(AB)
Therefore, R(AB)>=2+3-3=2;
Therefore, r (ab) = 2;
4.？ ( 1)r(A)？ =? n
(2)A has n linearly independent eigenvectors.
5. Let f (a) f(a)= b = a3-4a 2+2e；;
Because the eigenvalue of a is 1, 2,-1, so? The eigenvalue of a 2 is 1, 4,1; The eigenvalue of a 3 is 1, 8,-1.
So use the corresponding a 2 respectively? The eigenvalue of a 3 replaces a 2? Bring in a 3.
F (λ) = a 3-4a 2+2, and the eigenvalue of f(A) is 3,6,3, that is, the eigenvalue of B is-1,-6,3.
6.？ ( 1)
1- 1? 0
- 1? 1? 2
0? 2? five
(2)
Quadratic matrix? Answer? =
12t？ - 1
2t 12
- 125
Second-order sequential master-slave
12t
2t 1
=? 1? -? 4t^2
| One |? =? -? 20*t^2？ -? 8*t
So what? 1? -? 4t^2？ & gt0,? -? 20*t^2？ -? 8 * t & gt0
Solve? -2/5? & lt？ t？ & lt？ 0.
Second, multiple-choice questions: I will write the answers first, and ask me if you don't understand. I will give you a detailed answer tomorrow.
B
Nothing seems to be right.
3.A
4.C
5.B
6.B
7.A
8.D
9.C
10.C
1 1.A
12.A