Consider matrix `A=[a_(ij)]_(nxxn)`. Form the matrix `A-lamdal, lamda` being a number, real of complex.
`A-lamdal=[{:(a_11-lamda,a_12,...,a_(1n)),(s_21,a_22-lamda,...,a_(2n)),(...,...,...,...),(a_(n1),a_(n2),...,a_(n n)-lamda):}]`
Then det `(A-lamdaI)=(-1)^n[lamda^n+b_1lamda^(n-1)+b_2lamda^(n-2)+...+b_(n)]`.
An important rheorem tells us that the matrix A satisfies the equation `X^n+b_1x^(n-1)+b_2x^(n-2)+...+b_2=0.` This equation is called hte characteristic equation of A. For all the questions on theis passeage, take `A=[{:(1,4),(2,3):}]`
The matrix A satisfies the matrix equation

Consider matrix A=[a_(ij)]_(nxxn) . Form the matrix A-lamdal, lamda being a number, real of complex. A-lamdal=[{:(a_11-lamda,a_12,...,a_(1n)),(s_21,a_22-lamda,...,a_(2n)),(...,...,...,...),(a_(n1),a_(n2),...,a_(n n)-lamda):}] Then det (A-lamdaI)=(-1)^n[lamda^n+b_1lamda^(n-1)+b_2lamda^(n-2)+...+b_(n)] . An important rheorem tells us that the matrix A satisfies the equation X^n+b_1x^(n-1)+b_2x^(n-2)+...+b_2=0. This equation is called hte characteristic equation of A. For all the questions on theis passeage, take A=[{:(1,4),(2,3):}] Which of the follwing is inverse fo A ?

Consider matrix A=[a_(ij)]_(nxxn) . Form the matrix A-lamdal, lamda being a number, real of complex. A-lamdal=[{:(a_11-lamda,a_12,...,a_(1n)),(s_21,a_22-lamda,...,a_(2n)),(...,...,...,...),(a_(n1),a_(n2),...,a_(n n)-lamda):}] Then det (A-lamdaI)=(-1)^n[lamda^n+b_1lamda^(n-1)+b_2lamda^(n-2)+...+b_(n)] . An important rheorem tells us that the matrix A satisfies the equation X^n+b_1x^(n-1)+b_2x^(n-2)+...+b_2=0. This equation is called hte characteristic equation of A. For all the questions on theis passeage, take A=[{:(1,4),(2,3):}] Which of the follwing is inverse fo A ?

Consider matrix A=[a_(ij)]_(nxxn) . Form the matrix A-lamdal, lamda being a number, real of complex. A-lamdal=[{:(a_11-lamda,a_12,...,a_(1n)),(s_21,a_22-lamda,...,a_(2n)),(...,...,...,...),(a_(n1),a_(n2),...,a_(n n)-lamda):}] Then det (A-lamdaI)=(-1)^n[lamda^n+b_1lamda^(n-1)+b_2lamda^(n-2)+...+b_(n)] . An important rheorem tells us that the matrix A satisfies the equation X^n+b_1x^(n-1)+b_2x^(n-2)+...+b_2=0. This equation is called hte characteristic equation of A. For all the questions on theis passeage, take A=[{:(1,4),(2,3):}] The matrix A^5-4A^4-7A^3+11A^2-A-10 /, the expressed as a linear polynomial in A, is

B={a_(n):n in N,a_(n)+1=2a_(n) and a_(1)=3}

If |a_(i)|lt1lamda_(i)ge0 for i=1,2,3,.......nandlamda_(1)+lamda_(2)+.......+lamda_(n)=1 then the value of |lamda_(1)a_(1)+lamda_(2)a_(2)+.......+lamda_(n)a_(n)| is :

If |a_(i)|lt1lamda_(i)ge0 for i=1,2,3,.......nandlamda_(1)+lamda_(2)+.......+lamda_(n)=1 then the value of |lamda_(1)a_(1)+lamda_(2)a_(2)+.......+lamda_(n)a_(n)| is :

a_(0)x^(n) + a_(1)x^(n-1) + a_(2)x^(n-2) + ……..a_(n)x^(n) is polynomial of degree ……………

Let a_(0)/(n+1) +a_(1)/n + a_(2)/(n-1) + ….. +(a_(n)-1)/2 +a_(n)=0 . Show that there exists at least one real x between 0 and 1 such that a_(0)x^(n) + a_(1)x^(n-1) + …..+ a_(n)=0

If the polynomial equation a_(n)x^(n)+a_(n-1)x^(n-1)+a_(n-2)x^(n-2)+......+a_(0)=0,n being a positive integer,has two different real roots a and b. then between a and b the equation na_(n)x^(n-1)+(n-1)a_(n-1)x^(n-2)+......+a_(1)=0 has