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Matrices and DeterminantsQuestion and Answers: Page 2

Question Number 199001 Answers: 1 Comments: 0

If ,A ∈ M_(n×n) , A^( 2) = A ,1≠ k ∈R. Find ( I − kA )^( −1) = ?

$I f, A \in M_{n \times n}, A^{2} = A, 1 \neq k \in R .$ $F i n d {(I - k A)}^{- 1} = ?$

Question Number 198743 Answers: 1 Comments: 0

Question Number 198156 Answers: 1 Comments: 0

Prove that ((2t−1)/(lnt−ln(1−t)))=∫^( 1) _( 0) t^x (1−t)^(1−x) dx and ∫^( 1) _( 0) ((2t−1)/(lnt−ln(1−t)))dt = (π/2)∫^( 1) _( 0) ((x(1−x))/(sin(πx)))dx

$Prove that$ $\frac{2 t - 1}{lnt - \ln (1 - t)} = {\int_{0}}^{1} t^{x} {(1 - t)}^{1 - x} dx$ $and {\int_{0}}^{1} \frac{2 t - 1}{lnt - \ln (1 - t)} dt = \frac{π}{2} {\int_{0}}^{1} \frac{x (1 - x)}{\sin (π x)} dx$

Question Number 195203 Answers: 1 Comments: 0

Calculer ∫^( +∞) _( 0) (dt/((e^t −e^(−t) )^2 +a^2 ))

$Calculer {\int_{0}}^{+ \infty} \frac{dt}{{(e^{t} - e^{- t})}^{2} + a^{2}}$

Question Number 195185 Answers: 0 Comments: 0

1/ Montrer que ∫^( +∞) _( 0) (((1−x^2 )^(2p−1) )/(1−x^(4p) ))dx=((2^(2p−3) /p))π[1+2Σ_(k=1) ^(p−1) cos^(2p−1) (((kπ)/(2p)))] 2/ En de^ duire ∫^( 1) _( 0) (((1−x^2 )^(2p−1) )/(1−x^(4p) ))dx

$1 / Montrer que {\int_{0}}^{+ \infty} \frac{{(1 - x^{2})}^{2 p - 1}}{1 - x^{4 p}} d x = (\frac{2^{2 p - 3}}{p}) π [1 + 2 \underset{k = 1}{\sum^{p - 1}} {c o s}^{2 p - 1} (\frac{k π}{2 p})]$ $2 / En d \overset{´}{e d u i r e} {\int_{0}}^{1} \frac{{(1 - x^{2})}^{2 p - 1}}{1 - x^{4 p}} d x$

Question Number 194915 Answers: 2 Comments: 4

(3/(x−3))+(5/(x−5))+(7/(x−17))+((19)/(x−19))=x^2 −11x−4

$\frac{3}{x - 3} + \frac{5}{x - 5} + \frac{7}{x - 17} + \frac{19}{x - 19} = x^{2} - 11 x - 4$

Question Number 194642 Answers: 2 Comments: 0

If A= (((a b c)),((b c a)),((c a b)) ) and a,b,c >0 such that abc=1 and A^T .A=I find a^3 +b^3 +c^3 −3abc .

$If A = (\begin{matrix} a b c \\ b c a \\ c a b \end{matrix}) and a, b, c > 0$ $such that abc = 1 and A^{T} . A = I$ $find a^{3} + b^{3} + c^{3} - 3 abc .$

Question Number 192464 Answers: 0 Comments: 1

Question Number 191030 Answers: 1 Comments: 0

Question Number 190860 Answers: 0 Comments: 2

Question Number 190266 Answers: 1 Comments: 0

a ball is thrown vertically upward from a point 0.5m above the ground with speed u = 7m/s find the height reached above ground g = 10m/s^2

$a b a l l i s t h r o w n v e r t i c a l l y u p w a r d$ $f r o m a p o i n t 0.5 m a b o v e t h e g r o u n d w i t h$ $s p e e d u = 7 m / s$ $f i n d t h e h e i g h t r e a c h e d a b o v e g r o u n d$ $g = 10 m / s^{2}$

Question Number 183965 Answers: 1 Comments: 0

A linear transformation E, of the x−y plane is defined as E:(x, y) → (2x+y, 2x+3y) Find the equation of the line that remains invariant under the transformation.

$A linear transformation E, of the$ $x - y plane is defined as$ $E : (x, y) \to (2 x + y, 2 x + 3 y)$ $Find the equation of the line that$ $remains invariant under the$ $transformation .$

Question Number 183863 Answers: 1 Comments: 0

Question Number 183814 Answers: 1 Comments: 0

determine eigen values and eigen vectors for each λ . and verify Ax=λx A= [(((√3)/2),(−(1/2))),((1/2),( ((√3)/2))) ]

$d e t e r m i n e e i g e n v a l u e s a n d e i g e n v e c t o r s f o r$ $e a c h λ . a n d v e r i f y A x = λ x$ $A = [\begin{matrix} \frac{\sqrt{3}}{2} & - \frac{1}{2} \\ \frac{1}{2} & \frac{\sqrt{3}}{2} \end{matrix}]$

Question Number 183425 Answers: 0 Comments: 0

find the rank of the matrix A and B by following row operation: A= [(1,2,3,(−1)),((−2),(−1),(−3),(−1)),(1,0,1,( 1)),(0,1,1,(−1)) ] B= [(( 1),( 2),(−1),( 4)),(( 2),( 4),( 3),( 5)),((−1),(−2),( 6),(−7)) ]

$f i n d t h e r a n k o f t h e m a t r i x A a n d B b y$ $f o l l o w i n g r o w o p e r a t i o n :$ $A = [\begin{matrix} 1 & 2 & 3 & - 1 \\ - 2 & - 1 & - 3 & - 1 \\ 1 & 0 & 1 & 1 \\ 0 & 1 & 1 & - 1 \end{matrix}]$ $B = [\begin{matrix} 1 & 2 & - 1 & 4 \\ 2 & 4 & 3 & 5 \\ - 1 & - 2 & 6 & - 7 \end{matrix}]$

Question Number 183240 Answers: 1 Comments: 0

find the value of cofficent μ in the following system from the determinat: 2x_1 +μx_2 +x_3 =0 (μ−1)x_1 −x_2 +2x_3 =0 4x_1 +x^2 +4x^3 =0

$f i n d t h e v a l u e o f c o f f i c e n t μ i n t h e f o l l o w i n g$ $s y s t e m f r o m t h e d e t e r m i n a t :$ $2 x_{1} + μ x_{2} + x_{3} = 0$ $(μ - 1) x_{1} - x_{2} + 2 x_{3} = 0$ $4 x_{1} + x^{2} + 4 x^{3} = 0$

Question Number 183239 Answers: 0 Comments: 0

determine eigenvalues and digonalize by row operation [(4,(−9),6,(12)),(9,(−1),4,6),(2,(−11),8,(16)),((−1),( 3),0,(−1)) ]

$d e t e r m i n e e i g e n v a l u e s a n d d i g o n a l i z e$ $b y r o w o p e r a t i o n$ $[\begin{matrix} 4 & - 9 & 6 & 12 \\ 9 & - 1 & 4 & 6 \\ 2 & - 11 & 8 & 16 \\ - 1 & 3 & 0 & - 1 \end{matrix}]$

Question Number 182050 Answers: 1 Comments: 0

A= [(a,b,c),((−2),3,6),(0,(−2),5) ]and B= [(1,2,4),(0,3,9),((−1),2,2) ] A×B= [((−1),3,(−1)),((−8),d,(31)),((−5),4,e) ]find the missing value

$A = [\begin{matrix} a & b & c \\ - 2 & 3 & 6 \\ 0 & - 2 & 5 \end{matrix}] a n d B = [\begin{matrix} 1 & 2 & 4 \\ 0 & 3 & 9 \\ - 1 & 2 & 2 \end{matrix}]$ $A \times B = [\begin{matrix} - 1 & 3 & - 1 \\ - 8 & d & 31 \\ - 5 & 4 & e \end{matrix}] f i n d t h e m i s s i n g v a l u e$

Question Number 181836 Answers: 0 Comments: 0

∫_0 ^( 1) ∫_0 ^( 1) ((cos^(−1) (xy)sin^(−1) (xy))/(ln(xy)))dxdy

$\int_{0}^{1} \int_{0}^{1} \frac{{c o s}^{- 1} (x y) {s i n}^{- 1} (x y)}{l n (x y)} d x d y$

Question Number 181573 Answers: 0 Comments: 1

25^x − 4^x = 9^x fimd x

$25^{x} - 4^{x} = 9^{x}$ $f i m d x$

Question Number 180855 Answers: 0 Comments: 0

Find number of skew symmetric matrices of order 3×3 in which all non diagonal elements are different and belong to the set {−9,−8,−7,...,7,8,9}.

$F i n d n u m b e r o f s k e w s y m m e t r i c$ $m a t r i c e s o f o r d e r 3 \times 3 i n w h i c h$ $a l l n o n d i a g o n a l e l e m e n t s a r e$ $d i f f e r e n t a n d b e l o n g t o t h e$ $s e t {- 9, - 8, - 7, . . ., 7, 8, 9} .$

Question Number 176371 Answers: 0 Comments: 1

Question Number 175731 Answers: 0 Comments: 0

Question Number 175525 Answers: 0 Comments: 0

Question Number 175266 Answers: 0 Comments: 1

Find matrix ∣A∣A^(-1) given that matrix A= (((√2),(-1),1,( 0)),(4,3,2,(-1)),(0,2,3,( 1)),(1,(-1),0,( 1)) ) using row operations

$Find matrix ∣ A ∣ A^{- 1}$ $given that matrix$ $A = (\begin{matrix} \sqrt{2} & - 1 & 1 & 0 \\ 4 & 3 & 2 & - 1 \\ 0 & 2 & 3 & 1 \\ 1 & - 1 & 0 & 1 \end{matrix})$ $using row operations$

Question Number 175265 Answers: 1 Comments: 0

Given that matrix B= { (( (√3))),((-(√5))) :} {: (( (√2))),(( (√7))) } find B^(-1) using row operation

$Given that matrix$ $B = {\begin{cases} \sqrt{3} \\ - \sqrt{5} \end{cases} \begin{matrix} \sqrt{2} \\ \sqrt{7} \end{matrix}} find$ $B^{- 1} using row operation$

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