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Matrices and DeterminantsQuestion and Answers: Page 12

Question Number 2546 Answers: 0 Comments: 4

If A and B are two matrices of suitable order does there exist definition for A^B ?

$If A and B are two matrices of suitable order$ $does there exist definition for A^{B} ?$

Question Number 1771 Answers: 1 Comments: 0

2x−y+2z=4 x+10y−3z=10

$2 x - y + 2 z = 4$ $x + 10 y - 3 z = 10$

Question Number 605 Answers: 3 Comments: 1

Given a matrix A ∈ M_(n × n ) ∀ k ∈ N define: A= { ((∅_n if A=∅ and k≥1)),((I_n if A≠∅_n and k≠0)),((A^(k−1) A if A≠∅_n and k≥1)) :} Prove that A^k A^r =A^(k+r) ∀ k,r ∈ N.

$G i v e n a m a t r i x A \in M_{n \times n} \forall k \in N d e f i n e :$ $A = {\begin{cases} \emptyset_{n} i f A = \emptyset a n d k ⩾ 1 \\ I_{n} i f A \neq \emptyset_{n} a n d k \neq 0 \\ A^{k - 1} A i f A \neq \emptyset_{n} a n d k ⩾ 1 \end{cases}$ $P r o v e t h a t A^{k} A^{r} = A^{k + r} \forall k, r \in N .$

Question Number 529 Answers: 1 Comments: 0

Question Number 358 Answers: 1 Comments: 0

A= [(x,(−y)),(y,x) ] X= [(x),(y) ] Y=AX

$A = [\begin{matrix} x & - y \\ y & x \end{matrix}]$ $X = [\begin{matrix} x \\ y \end{matrix}]$ $Y = AX$

Question Number 346 Answers: 1 Comments: 0

Γ(θ)= [((cos θ),(sin θ)),((−sin θ),(cos θ)) ] Λ(θ,t)= [((cos θ),(sinh t sin θ)),((sin θ),(cosh t cos θ)) ] ζ(θ,t)=Γ(θ)×Λ(θ,t)+Λ(θ,t)×Γ(θ) ζ(θ,0)=? det ζ(θ,0)=?

$Γ (θ) = [\begin{matrix} \cos θ & \sin θ \\ - \sin θ & \cos θ \end{matrix}]$ $Λ (θ, t) = [\begin{matrix} \cos θ & \sinh t \sin θ \\ \sin θ & \cosh t \cos θ \end{matrix}]$ $ζ (θ, t) = Γ (θ) \times Λ (θ, t) + Λ (θ, t) \times Γ (θ)$ $ζ (θ, 0) = ?$ $\det ζ (θ, 0) = ?$

Question Number 275 Answers: 1 Comments: 0

6867865396÷678

$6867865396 \div 678$

Question Number 15 Answers: 1 Comments: 0

If A= [(( 3),(−5)),((−4),( 2)) ], show that A^2 −5A−14I=0

$If A = [\begin{matrix} 3 & - 5 \\ - 4 & 2 \end{matrix}],$ $show that A^{2} - 5 A - 14 I = 0$

Question Number 13 Answers: 1 Comments: 0

Expand the determnent △= determinant ((a,h,g),(h,b,f),(g,f,c))

$Expand the determnent$ $△ = | \begin{matrix} a & h & g \\ h & b & f \\ g & f & c \end{matrix} |$

Question Number 11 Answers: 1 Comments: 0

Evaluate: determinant (((x^2 −x+1),(x−1)),(( x+1),(x+1)))

$Evaluate :$ $| \begin{matrix} x^{2} - x + 1 & x - 1 \\ x + 1 & x + 1 \end{matrix} |$

Question Number 9 Answers: 1 Comments: 0

Let A= [(( 0),(−tan(x/2))),((tan(x/2)),( 0)) ] and I is the identity matrix of order 2. Show that (I+A)=(I−A)∙ [((cos x),(−sin x)),((sin x),( cos x)) ].

$Let A = [\begin{matrix} 0 & - \tan \frac{x}{2} \\ \tan \frac{x}{2} & 0 \end{matrix}] and I is the$ $identity matrix of order 2 . Show that$ $(I + A) = (I - A) \cdot [\begin{matrix} \cos x & - \sin x \\ \sin x & \cos x \end{matrix}] .$

Question Number 7 Answers: 1 Comments: 0

If A= [(2,1,3),(4,1,0) ]and B= [(1,(−1)),(0,2),(5,0) ], verify that (AB)′=B′A′

$If A = [\begin{matrix} 2 & 1 & 3 \\ 4 & 1 & 0 \end{matrix}] a n d B = [\begin{matrix} 1 & - 1 \\ 0 & 2 \\ 5 & 0 \end{matrix}],$ $verify that {(A B)}^{'} = B^{'} A^{'}$

Pg 7 Pg 8 Pg 9 Pg 10 Pg 11 Pg 12

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