Algorithms for linear algebra calculation problems, linear algebra calculation problems

Solution: a =

1 -2 3k

1 2k -3

k -2 3

r2+r1, r3-kr1

1 -2 3k

0 2k-2 3k-3

0 2k-2 -3k^2+3

r3-r21 -2 3k

0 2(k-1) 3(k-1) (

0 0 -3(k-1)(k+2)

It is easy to know that when k=1, r(a)=1

When k=-2, r(a)=2

At this point, a --

So when k=-2, r(a)=2

Note: This question can be considered|a|=0

However, the calculation |a|, still to form the upper triangle (*), and then to change the trapezoid, the calculation repeats!

When r(a)=1, the determinant of a must be 0, and det(a)=0 is an equation about k, which can be solved to obtain the possible k

And det(a)=0 can have three cases, r(a)=0, r(a)=1, r(a)=2, you can bring in each k to see which satisfies r(a)=1.

The algorithm is to simplify the determinant, and |a|=0 is then used as an equation to find the root, but it needs to be brought into the calculation.

It can also be directly reduced to the simplest ladder form by the elementary variation method, and then evaluated according to the rank.

If you want me, just sort it out into a ladder type, and then figure it out.

Summary. Hello dear, this question is done by me, it takes a little time to type, and please be patient and don't go away

Hello dear, this question is done by me, it takes a little time to type, and please be patient and don't go away

Hello, dear (* Xiao Ran is at your service, oh <>

Send it over<>

Wait a minute, the last step is the Van der Mon determinant calculation

According to the definition of linear correlation, the question can be set c1, c2c1*k+c2*2=1

c1*2+c2*k=-1

c1*1+c2*0=1

The solution yields c1=1, c2=-1, and k=3

Linear independence is the opposite of linear correlation.

i.e. k is not equal to 3

AnswerLinear algebra is a branch of mathematics that deals with vectors, vector spaces (or linear spaces), linear transformations, and systems of linear equations of finite dimensions. Vector space is an important topic in modern mathematics. Therefore, linear algebra is widely used in abstract algebra and functional analysis. Through analytic geometry, linear algebra can be concretely represented. The theory of linear algebra has been generalized to operator theory.

Since nonlinear models in scientific research can often be approximated as linear models, linear algebra is widely used in natural sciences and social sciences.

|a|=

1 -2 3k|

1 2k -3|

k -2 3|, add -1 and k times of the first row to the first.

Two or three lines, got.

1 -2 3k

0 2k+2 -3k-3

0 -2k-2 3k^2+3,-(2k+2)(3k^2+3)+(3k-3)(-2k-2)=-6(k+1)(k^2-k)

6k(k+1)(k-1),1) no solution.

2) k=0, soil 1

matrix a=(1 -1 0 1 2; 1 -2 1 4 3 ;2 -3 1 5 5) Add the negative double of the first row to the second line, and add the negative two times of the first row to the third line to become (1 -1 0 1 2;0 -1 1 3 1 ；0 -1 1 3 1) and then double the minus of the second row to the third row and it becomes (1 -1 0 1 2 ; 0 1 -1 -3 -1 ；0 0 0 0 0）

Because r(a)=r(a) solves the basic solution system a1=(2,3,0,1) t a2=(1 1 1 0) t and the general solution b=(1 -1 0 0) t

Therefore, the solution is k1(2 3 0 1) t+k2(1 1 1 0)t+(1 -1 0 0) t, and the solution is transposed.

You should take a picture of ** and pass it up.,You really can't understand this.。。。 It's messed up.

The power of the diagonal array is equal to the diagonal array formed by the power of all its diagonal elements.

a = (a1, a2, a3, a4) = [1 0 0 2][0 1 0 -1][0 0 1 3][1 -1 -1 0]

1 0 0 2][0 1 0 -1][0 0 1 3][0 -1 -1 -2] primary row transformation.

1 0 0 2][0 1 0 -1][0 0 1 3][0 0 -1 -3] primary row transformation.

1 0 0 2][0 1 0 -1][0 0 1 3][0 0 0 0]a1, a2, a3 is a maximally linear independent group, a4 = 2a1 - a2 + 3a3