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# Let A aud B be n following identity:matrices ad B; be the ith column 0l B for = [We want t0 prove thedet([ABB,] +det([Bi ABzBa]~det([BABa] = tr(A) det (BIF You S pr...

## Question

###### Let A aud B be n following identity:matrices ad B; be the ith column 0l B for = [We want t0 prove thedet([ABB,] +det([Bi ABzBa]~det([BABa] = tr(A) det (BIF You S prore the above dlirectly; do it . Otherwise follow the following steps;Show that for any fixed B the mapping T : R"x" _ R defined byT(A) = det([ABBal det([B AB,B,]det( [B1AB,]linear transformation; Let {E;j:i.j=1,2 "} be the standard basis of R"xn where E,j is the n X n matrix with in the (i. j)-entry and with 0 in

Let A aud B be n following identity: matrices ad B; be the ith column 0l B for = [ We want t0 prove the det([AB B,] +det([Bi ABz Ba] ~det([B ABa] = tr(A) det (B IF You S prore the above dlirectly; do it . Otherwise follow the following steps; Show that for any fixed B the mapping T : R"x" _ R defined by T(A) = det([AB Bal det([B AB, B,] det( [B1 AB,] linear transformation; Let {E;j:i.j=1,2 "} be the standard basis of R"xn where E,j is the n X n matrix with in the (i. j)-entry and with 0 in other entries_ Show that T(E;;) tr(E;j) det(B). Show that T(A) tr( A) dlet ( B).  #### Similar Solved Questions

##### Assigument 286_ 1s 2r - pnme Or ureducible over Rlr]? WRot about OVer Qll? Oeer Zll? Howr about Fa these rings?
Assigument 286_ 1s 2r - pnme Or ureducible over Rlr]? WRot about OVer Qll? Oeer Zll? Howr about Fa these rings?...
##### The followingtwo-way table describing the age and marital status of American women in 1995_Marital Status Married Widowed 0306 00uzAge (Years) Never Married Divorced Total 18-24 0933 0026 1267 25-39 0342 3213 0698 3686 40-64 023- 1834 264 007. 0780 103 L.0O Total 939 5917 If a randomly selected American woman Was under the age of 40 years old, what is the probability that she was never married?2712 '3641 0698 8412 1631 0869
The following two-way table describing the age and marital status of American women in 1995_ Marital Status Married Widowed 0306 00uz Age (Years) Never Married Divorced Total 18-24 0933 0026 1267 25-39 0342 3213 0698 3686 40-64 023- 1834 264 007. 0780 103 L.0O Total 939 5917 If a randomly selected A...
##### Find to two decimal places, the area of the surfaces generated by revolving the curve y 3sinx in 0<Xsr about the X-axis_The area of the surface is (Simplify your answer: Type an integer or decimal rounded to two decimal places as needed:)
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##### Sales growth_ marketing researcher studied annual sales 0f product that had been introduced 10 years ago. The data are as follows, where Xis the year (coded) and Yis sales in thousands of units:283300Prepare scatter plot of the data Does linear relation appear adequate here?b. Use the Box-Cox procedure and standardization (3.36) to find an appropriate power transformation of Y Evaluate SSE for A = 5,.6, .7. What transformation of Yis suggested?Use the transformation Y' -VY and obtain the es
Sales growth_ marketing researcher studied annual sales 0f product that had been introduced 10 years ago. The data are as follows, where Xis the year (coded) and Yis sales in thousands of units: 283 300 Prepare scatter plot of the data Does linear relation appear adequate here? b. Use the Box-Cox pr...
##### Solution iS prepared by adding 0.10 mol of potassium acetate. KCH;COO. to [.00 L of water; Which statement about the solution correct?The solution is basic. B. The solution is neutral. C. The solution is acidic D. The concentrations of polassium ions and acetate ions will be identical. The concentration of acetate ions will be greater than the concentration of potassium ions:What is the pH ofa buffer that consists of045 M CH COOH and 0.35 M CH COONa? 1.8 10"A. 4,49 4.64 C. 4.85 D 5.00 E.5.5
solution iS prepared by adding 0.10 mol of potassium acetate. KCH;COO. to [.00 L of water; Which statement about the solution correct? The solution is basic. B. The solution is neutral. C. The solution is acidic D. The concentrations of polassium ions and acetate ions will be identical. The concentr...
##### The Fibonacci sequence is defined by V"-1+ V-2 for n 2 2 with starting values Vo and Vi Observe that the calculation of V requires the calculation of V. Va; . Vi-1. 'To avoid this. could this problem be written as eigenvalue problem adl solved for Va directly? If ~. find the explicit formla for 13)
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##### (a) Bound the error in the approximation$$sin (x) approx x$$for $-pi / 4 leq x leq pi / 4$.(b) Since this is a good approximation for small values of $x$, also consider the "percentage error"$$frac{sin (x)-x}{sin (x)} approx frac{sin (x)-x}{x}$$Bound the absolute value of the latter quantity for $-delta leq x leq delta .$ Pick $delta$ to make the absolute value of the percentage error less than $1 %$.
(a) Bound the error in the approximation $$sin (x) approx x$$ for $-pi / 4 leq x leq pi / 4$. (b) Since this is a good approximation for small values of $x$, also consider the "percentage error" $$frac{sin (x)-x}{sin (x)} approx frac{sin (x)-x}{x}$$ Bound the absolute value of the latt...
##### Find the indefinite (part a and b) and definite (part c) integrals by hand: Show all of your work for full credita) f 3t2 (t8 _ 5) 9 dtb) dx (52+1)c) 55 (28 2x + 4) dx
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##### In Exercises $35-46,$ determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial.$$x^{2}- rac{2}{3} x$$
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##### Titanium is a very reactive metal. Explain why titanium has a high corrosion resistance to seawater and can be used for the production of ship components.
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##### Problem 4 A 65 m wide river flows from north to south at speed of 3,4 mls: swimmer swims relative t0 the watcr at rate of 4.8 mls aiming aeross the river at an angle of 268 north of east. What is the spced of the swimmer with respect to the shore? How far downstream (south) , from point directly across the river, does the swimmer hit the shore? points)
Problem 4 A 65 m wide river flows from north to south at speed of 3,4 mls: swimmer swims relative t0 the watcr at rate of 4.8 mls aiming aeross the river at an angle of 268 north of east. What is the spced of the swimmer with respect to the shore? How far downstream (south) , from point directly acr...
##### To strengthen his arm and chest muscles, an 75 kg k g athlete2.0 m m tall is doing a series of push-ups as shown in the figurebelow (Figure 1). His center of mass is 1.20 m m from the bottom ofhis feet, and the centers of his palms are 30.0 cm c m from the topof his head.Find the force that the floor exerts on each of his feet,assuming that both feet exert the same force.
To strengthen his arm and chest muscles, an 75 kg k g athlete 2.0 m m tall is doing a series of push-ups as shown in the figure below (Figure 1). His center of mass is 1.20 m m from the bottom of his feet, and the centers of his palms are 30.0 cm c m from the top of his head. Find the force that the...
##### "GuaVn ' N V"t2n n(" + 4) +(20
"Gua Vn ' N V" t2n n(" + 4) +(20...
##### QUESTION 3Tanocn variable which can take onlychne values 5 0.6,tne 2-nd momentaboutthe origin p*2 7.21 b. 53.29 39,64 36.78and wich probabilizy distriburion f{5) 0.18, f(6) 0.03,f{7) = 0.19,and f(8)=
QUESTION 3 Tanocn variable which can take onlychne values 5 0.6,tne 2-nd momentaboutthe origin p*2 7.21 b. 53.29 39,64 36.78 and wich probabilizy distriburion f{5) 0.18, f(6) 0.03,f{7) = 0.19,and f(8)=...
##### An212 value(s) of 0 ofthe inclined plane such Ika The 2-59 Find out the rest On the wedge of mass Mzas 7304" hat He mass m remains at :small block and the figure-2.215, Friction between the wele and all other surface are smooth: plane is HFigure 2.215Naplg 4(p2 +42 Ams: [sin &, Xull 2(p'2qrMig where p m(g He) 9 = mla + pg) ra M; (a - g) and ( = W+iW + 'W Jark2 4 +k Mn? _ 12) -2kn sin @ Inun 2(/2 +k2 ) where Mig mla Kg) k a mlg Ha} n = M, (a - g) and a = M, + Mz+m
An 212 value(s) of 0 ofthe inclined plane such Ika The 2-59 Find out the rest On the wedge of mass Mzas 7304" hat He mass m remains at :small block and the figure-2.215, Friction between the wele and all other surface are smooth: plane is H Figure 2.215 Naplg 4(p2 +42 Ams: [sin &, Xull 2(p&...