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Matrices and DeterminantsQuestion and Answers: Page 10

Question Number 28678 Answers: 0 Comments: 0

let give A= (((1 (α/n))),((−(α/n) 1)) ) with n ∈N^∗ and α∈R find lim_(n→+∞) A^n .

$l e t g i v e A = (\begin{matrix} 1 \frac{α}{n} \\ - \frac{α}{n} 1 \end{matrix})$ $w i t h n \in N^{*} a n d α \in R f i n d {l i m}_{n \to + \infty} A^{n} .$

Question Number 28261 Answers: 0 Comments: 0

let give the matrice ( 0 cosθ cos(2θ)) A= ( cosθ 0 cos(2θ) ) ( cos(θ) cos(2θ 0 ) and D_θ =det A solve inside R D_θ =0

$l e t g i v e t h e m a t r i c e$ $(0 c o s θ c o s (2 θ))$ $A = (c o s θ 0 c o s (2 θ))$ $(c o s (θ) c o s (2 θ 0)$ $a n d D_{θ} = d e t A s o l v e i n s i d e R D_{θ} = 0$

Question Number 28260 Answers: 0 Comments: 0

let give ( 1 1 −1) A= ( 1 1 1 ) ( −1 1 1 ) and the matrices I= ( 1 0 0 ) ( 0 1 1 ) ( 0 0 1 ) and J= ( 0 1 −1) ( 1 0 1). ( −1 1 0) 1) find J^2 and J^(−1) . 2) let put J^n = x_n I +y_n J .prove that x_(n+2 ) +x_(n+1) −2x_n =0 3) calculate J^n and A^n .

$l e t g i v e (1 1 - 1)$ $A = (1 1 1)$ $(- 1 1 1)$ $a n d t h e m a t r i c e s I = (1 0 0)$ $(0 1 1)$ $(0 0 1)$ $a n d J = (0 1 - 1)$ $(1 0 1) .$ $(- 1 1 0)$ $1) f i n d J^{2} a n d J^{- 1} .$ $2) l e t p u t J^{n} = x_{n} I + y_{n} J . p r o v e t h a t$ $x_{n + 2} + x_{n + 1} - 2 x_{n} = 0$ $3) c a l c u l a t e J^{n} a n d A^{n} .$

Question Number 28259 Answers: 0 Comments: 0

let give A= ( cosθ −sinθ ) ( sinθ cosθ ) 1) calculate^t A. A .prove that A is inversible and find A^(−1) 2) find A^n for n∈ N 3) developp (A +A^(−1) )^n then prove that 2^n cos^n θ = Σ_(k=0) ^n C_n ^k (n−2k)θ and Σ_(k=0) ^n C_n ^n sin(n−2k)θ =0 .

$l e t g i v e A = (c o s θ - s i n θ)$ $(s i n θ c o s θ)$ $1) c a l c u l a t e^{t} A . A . p r o v e t h a t A i s i n v e r s i b l e a n d f i n d$ $A^{- 1}$ $2) f i n d A^{n} f o r n \in N$ $3) d e v e l o p p {(A + A^{- 1})}^{n} t h e n p r o v e t h a t$ $2^{n} {c o s}^{n} θ = \sum_{k = 0}^{n} C_{n}^{k} (n - 2 k) θ a n d$ $\sum_{k = 0}^{n} C_{n}^{n} s i n (n - 2 k) θ = 0 .$

Question Number 28258 Answers: 0 Comments: 1

let give A = ( 1 1 ) ( 2 −1) find e^(A ) and e^(−tA) .

$l e t g i v e A = (1 1)$ $(2 - 1)$ $f i n d e^{A} a n d e^{- t A} .$

Question Number 28257 Answers: 0 Comments: 0

let give ( 2 3 −3) A = ( −1 0 1) ( −1 1 0 ) find a diagoal matrice D and a inversible matrice P wich verify A = P.D.P^(−1) and calculate A^n .

$l e t g i v e$ $(2 3 - 3)$ $A = (- 1 0 1)$ $(- 1 1 0)$ $f i n d a d i a g o a l m a t r i c e D a n d a i n v e r s i b l e m a t r i c e P w i c h$ $v e r i f y A = P . D . P^{- 1} a n d c a l c u l a t e A^{n} .$

Question Number 28255 Answers: 0 Comments: 0

let give p=(_(1 −2) ^(1 −1) ) and D= (_(3 −6) ^(2 −2) ) calculate A= p.D.p^(−1) .

$l e t g i v e p = (_{1 - 2}^{1 - 1}) a n d D = (_{3 - 6}^{2 - 2}) c a l c u l a t e$ $A = p . D . p^{- 1} .$

Question Number 28256 Answers: 0 Comments: 0

let give A= _( () −1 1 1) ( 1 −1 1) find A^n for n integr. ( 1 1 −1)

$l e t g i v e A =_{(} - 1 1 1)$ $(1 - 1 1) f i n d A^{n} f o r n i n t e g r .$ $(1 1 - 1)$

Question Number 27365 Answers: 0 Comments: 0

Question Number 27343 Answers: 1 Comments: 7

let give A=(_(2 2) ^(1 2) ) find A^n and e^A and e^(tA) . we remind that e^A = Σ_ (A^n /(n!))

$l e t g i v e A = (_{2 2}^{1 2}) f i n d A^{n} a n d e^{A}$ $a n d e^{t A} . w e r e m i n d t h a t e^{A} = \sum_{} \frac{A^{n}}{n!}$

Question Number 26264 Answers: 1 Comments: 0

(x/3)+2x=14

$\frac{x}{3} + 2 x = 14$

Question Number 25975 Answers: 1 Comments: 0

Question Number 25623 Answers: 1 Comments: 0

solve for A and B if 2A+B [((6 3)),((6 −2)) ] and 3A+2B [((1 0)),((0 5)) ]

$s o l v e f o r A a n d B i f 2 A + B [\begin{matrix} 6 3 \\ 6 - 2 \end{matrix}]$ $a n d 3 A + 2 B [\begin{matrix} 1 0 \\ 0 5 \end{matrix}]$

Question Number 24152 Answers: 0 Comments: 1

Let matrice A = ((a,b),(c,d) ), and A^T = A^(−1) Find d − bc

$Let matrice A = (\begin{matrix} a & b \\ c & d \end{matrix}), and A^{T} = A^{- 1}$ $Find d - b c$

Question Number 23358 Answers: 0 Comments: 0

Question Number 22930 Answers: 1 Comments: 0

Question Number 22700 Answers: 0 Comments: 0

Question Number 22432 Answers: 0 Comments: 0

(((5 3)),((3 2)) )A + (((2 5)),((5 1)) ) = (((4 7)),((6 2)) ) Find ∣4A^(−1) ∣

$(\begin{matrix} 5 3 \\ 3 2 \end{matrix}) A + (\begin{matrix} 2 5 \\ 5 1 \end{matrix}) = (\begin{matrix} 4 7 \\ 6 2 \end{matrix})$ $Find ∣ 4 A^{- 1} ∣$

Question Number 22386 Answers: 0 Comments: 0

equivalent matrices are obtained by

$e q u i v a l e n t m a t r i c e s a r e o b t a i n e d b y$

Question Number 19589 Answers: 1 Comments: 0

Let A and B is 3×3 matrix of equal number where A=symmetric matrix ....B=skew symmetric matrix and the relation... (A+B)(A−B)=(A−B)(A+B) then..the value of.. ... k (AB)^T =(−1)^k (AB) (a) −1 (c) 2 (b) 1 (d) 3

$L e t A a n d B i s 3 \times 3 m a t r i x o f e q u a l n u m b e r$ $w h e r e A = s y m m e t r i c m a t r i x$ $. . . . B = s k e w s y m m e t r i c m a t r i x$ $a n d t h e r e l a t i o n . . . (A + B) (A - B) = (A - B) (A + B)$ $t h e n . . t h e v a l u e o f . . . . . k$ ${(A B)}^{T} = {(- 1)}^{k} (A B)$ $(a) - 1 (c) 2$ $(b) 1 (d) 3$

Question Number 19547 Answers: 0 Comments: 2

A matrix has N rows and 2k−1 columns. Each column is filled with M ones and N−M zeros. A given row j is “cool” if and only if Σ_(i=1) ^(2k−1) a_(ji) ≥ k. Find the minimum and the maximum number of cool rows for given N, k and M.

$A matrix has N rows and 2 k - 1$ $columns . Each column is filled with$ $M ones and N - M zeros .$ $A given row j is ‘ ‘ {c o o l}^{″} if and only if$ $\underset{i = 1}{\sum^{2 k - 1}} a_{j i} ⩾ k . Find the minimum and$ $the maximum number of cool rows$ $for given N, k and M .$

Question Number 17890 Answers: 0 Comments: 0

Question Number 12046 Answers: 1 Comments: 0

how much matrices of integers number A= [(a,b),(c,d) ]if A^2 +A=2I, c=0, det(A)=4

$h o w m u c h m a t r i c e s o f i n t e g e r s n u m b e r$ $A = [\begin{matrix} a & b \\ c & d \end{matrix}] i f A^{2} + A = 2 I, c = 0, d e t (A) = 4$

Question Number 12044 Answers: 1 Comments: 0

A∈M_(n×n) A^2 =A (I+A)^(−1) =....???

$A \in M_{n \times n}$ $A^{2} = A$ ${(I + A)}^{- 1} = . . . . ? ? ?$

Question Number 11958 Answers: 0 Comments: 1

A∈M_(2016×2016) with the entries a_(ij) {_(0, if i+j≠2016) ^(1, if i+j=2016) find the determinant??

$A \in M_{2016 \times 2016}$ $w i t h t h e e n t r i e s a_{i j} {_{0, i f i + j \neq 2016}^{1, i f i + j = 2016}$ $f i n d t h e d e t e r m i n a n t ? ?$

Question Number 11353 Answers: 0 Comments: 0

reduce the matrix below to echelon form and then to row canonical form A = [((2 4 2 −2 5 1)),((3 6 2 2 0 4)),((4 8 2 6 −5 7)) ]

$reduce the matrix below to echelon form and then to row canonical form$ $A = [\begin{matrix} 2 4 2 - 2 5 1 \\ 3 6 2 2 0 4 \\ 4 8 2 6 - 5 7 \end{matrix}]$

Pg 5 Pg 6 Pg 7 Pg 8 Pg 9 Pg 10 Pg 11 Pg 12

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