## Question

###### Let $V$ be a vector space over a field $mathrm{F}$ such that $V=V_{1} oplus V_{2}$ for subspaces $V_{1}$ and $V_{2}$ of $V$. If $f_{1}$ and $f_{2}$ are bilinear forms on $V_{1}$ and $V_{2}$, respectively, prove that there is a unique bilinear form $f$ on $V$ whose restrictions to $V_{1}$ and $V_{2}$ are $f_{1}$ and $f_{2}$, respectively.

Let $V$ be a vector space over a field $mathrm{F}$ such that $V=V_{1} oplus V_{2}$ for subspaces $V_{1}$ and $V_{2}$ of $V$. If $f_{1}$ and $f_{2}$ are bilinear forms on $V_{1}$ and $V_{2}$, respectively, prove that there is a unique bilinear form $f$ on $V$ whose restrictions to $V_{1}$ and $V_{2}$ are $f_{1}$ and $f_{2}$, respectively.

## Answers

#### Similar Solved Questions

5 answers

##### 11 For each of these rate laws, state the reaction order with respect to the hypothetical subbstances Aand B, and give the overall order (a) Rate KAJIE]- Ib): Rate = k[A] [B] I(c:) rate k[B]? [Ajol

11 For each of these rate laws, state the reaction order with respect to the hypothetical subbstances Aand B, and give the overall order (a) Rate KAJIE]- Ib): Rate = k[A] [B] I(c:) rate k[B]? [Ajol...

5 answers

##### (12 points) Evaluate 6y dr + 2r dy; where C is the part of the graph of y = 12 going from (0,0) to (2,4) Hint: {se I as the parameter:

(12 points) Evaluate 6y dr + 2r dy; where C is the part of the graph of y = 12 going from (0,0) to (2,4) Hint: {se I as the parameter:...

5 answers

##### 0/8 points Previous AnswersLarColAIgRMRP7 4.5.501.XPComplete the table for savings account in which interest is compounded continuously.Initial InvestmentAnnual % RateTime to DoubleAmount After 10 years519001.79years$80014 years$200years$300.101.69years$2100.00Need Help?Read ItWatch It

0/8 points Previous Answers LarColAIgRMRP7 4.5.501.XP Complete the table for savings account in which interest is compounded continuously. Initial Investment Annual % Rate Time to Double Amount After 10 years 51900 1.79 years $800 14 years $200 years $300.10 1.69 years $2100.00 Need Help? Read It Wa...

5 answers

##### MLa Flz) = f(f(r))and GKi) (F(c))? aro suppose Ihal f(9) = 8. 0(8) W2,w{"(8) 5S f'(91 =13 Foi, F(S)eC"(9) F(T 0(7

mLa Flz) = f(f(r))and GKi) (F(c))? aro suppose Ihal f(9) = 8. 0(8) W2,w{"(8) 5S f'(91 =13 Foi, F(S)eC"(9) F(T 0(7...

4 answers

##### Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform: (Write your answer as a function of t.) s2 + 1 s(s - 1)(s + 1)(s - 4)

Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform: (Write your answer as a function of t.) s2 + 1 s(s - 1)(s + 1)(s - 4)...

5 answers

##### Math 112 Fall 2019Homework: Section 5.3 Homework Score: 0 of pt 9 of 115.3.21Use Heron'$ area formula to find the area of the triangle with the given side lengths 346 b = 239 c=425What is the area of the triangle?(Simplify your answer Type an integer Or & decimal Round t the nearest tenth if ne

Math 112 Fall 2019 Homework: Section 5.3 Homework Score: 0 of pt 9 of 11 5.3.21 Use Heron'$ area formula to find the area of the triangle with the given side lengths 346 b = 239 c=425 What is the area of the triangle? (Simplify your answer Type an integer Or & decimal Round t the nearest te...

5 answers

##### Prove by induction that:for n>0An+11455.9(4n-3)(4n+1)

Prove by induction that: for n>0 An+1 145 5.9 (4n-3)(4n+1)...

5 answers

##### The volume of a solid region E is equal t0 JJwz dv [[ [ et+" sin = dzdydr =[ &" dx:[d & dy:[L sinz d Let R be the unit circle centered at (0, 0). Then IJx(r?+)dA =Jz [3 drdo . The sets X(r,0,=) : r = 2} and {(p,0,0) : 0 = =/4} represent the same surface:

The volume of a solid region E is equal t0 JJwz dv [[ [ et+" sin = dzdydr =[ &" dx:[d & dy:[L sinz d Let R be the unit circle centered at (0, 0). Then IJx(r?+)dA =Jz [3 drdo . The sets X(r,0,=) : r = 2} and {(p,0,0) : 0 = =/4} represent the same surface:...

3 answers

##### To improve the accuracy f our linearfit berween absorbance and concertration,addan extra daza pointio your linear regressicn where you make the assumption that pure wazer hasan abzcrbance 0f zero, bmake sure -natyCu chooze Linea Rezres? curvefi ensure thatthere arero air bubblesinthe Cuvette, use tne data points only #3 tne lower end ofthe concentration rarze because Beer's Lawisnotapplicable forhizher corcentraticrs

To improve the accuracy f our linearfit berween absorbance and concertration, addan extra daza pointio your linear regressicn where you make the assumption that pure wazer hasan abzcrbance 0f zero, bmake sure -natyCu chooze Linea Rezres? curvefi ensure thatthere arero air bubblesinthe Cuvette, use t...

5 answers

##### Suppose that a function $f(z)$ has a power series representation$$f(z)=sum_{n=0}^{infty} a_{n}left(z-z_{0}ight)^{n}$$inside some circle $left|z-z_{0}ight|=R .$ Use Theorem 2 in Sec. 71, regarding term by term differentiation of such a series, and mathematical induction to show that$$f^{(n)}(z)=sum_{k=0}^{infty} frac{(n+k) !}{k !} a_{n+k}left(z-z_{0}ight)^{k} quad(n=0,1,2, ldots)$$when $left|z-z_{0}ight|<R$. Then, by setting $z=z_{0}$, show that the coefficients $a_{n}(n=0,1,2, ldots)$ are the

Suppose that a function $f(z)$ has a power series representation $$ f(z)=sum_{n=0}^{infty} a_{n}left(z-z_{0} ight)^{n} $$ inside some circle $left|z-z_{0} ight|=R .$ Use Theorem 2 in Sec. 71, regarding term by term differentiation of such a series, and mathematical induction to show that $$ f^{(n)}(...

1 answers

##### Sometimes finding the extrema for a function of two variables can best be handled by commonsense methods using a computer. To illustrate, look at the pictures of the surfaces and the corresponding contour maps for the five functions graphed in Fig. ures $15-19$ of Section 12.1. Note that these graphs suggest that we can locate the extrema visually. With the additional ability to evaluate the function at points, we can experimentally approximate maxima and minima with good accuracy. Use your tech

Sometimes finding the extrema for a function of two variables can best be handled by commonsense methods using a computer. To illustrate, look at the pictures of the surfaces and the corresponding contour maps for the five functions graphed in Fig. ures $15-19$ of Section 12.1. Note that these graph...

5 answers

##### Use Figure $16-11$ to explain why Friedel-Crafts alkylations often give polysubstitution but Friedel-Crafts acylations do not.

Use Figure $16-11$ to explain why Friedel-Crafts alkylations often give polysubstitution but Friedel-Crafts acylations do not....

1 answers

##### Evaluate the integral. $$ \int \frac{d x}{x^{2}-3 x-4} $$

Evaluate the integral. $$ \int \frac{d x}{x^{2}-3 x-4} $$...

5 answers

##### On returning from a trip overseas, an individual withpersistent diarrhea is diagnosed as having an E.histolytica infection. Fecal examination reveals thepresence of blood in the stool, suggesting damage to the intestinalmucosa. Explain why and how the mucosa was compromised by thisparasite.

On returning from a trip overseas, an individual with persistent diarrhea is diagnosed as having an E. histolytica infection. Fecal examination reveals the presence of blood in the stool, suggesting damage to the intestinal mucosa. Explain why and how the mucosa was compromised by this parasite....

5 answers

##### UrV ARIhlu equahtSole446I0 ' I0' -0" _ Io" =13. I0 * I0' -14. 10' * I0 '_IS 10"/ I0J =>"?17. Solie for A. |54 1.71 = -3.98 18. ( -L.1OX7.14-11.03)

UrV ARIhlu equaht Sole 446 I0 ' I0' - 0" _ Io" = 13. I0 * I0' - 14. 10' * I0 '_ IS 10"/ I0J = >"? 17. Solie for A. |54 1.71 = -3.98 18. ( -L.1OX7.14-11.03)...

5 answers

##### Indicate the concentration of each ion present in the solutionformed by mixing the following. (Assume that the volumes areadditive.)(a) 50 mL of 0.100 M HCl and 10.0mL of 0.520 M HClH+________ MCl -_________ M(b) 15.0 mLof 0.316 M Na2SO4 and 35.4 mLof 0.200 M KClNa+______ MK+ _______MSO42-________ MCl -________ M(c) 3.50 g of NaCl in 55.9 mLof 0.511 M CaCl2 solutionNa+_______ MCa2+ ______MCl -______ M

Indicate the concentration of each ion present in the solution formed by mixing the following. (Assume that the volumes are additive.) (a) 50 mL of 0.100 M HCl and 10.0 mL of 0.520 M HCl H+ ________ M Cl - _________ M (b) 15.0 mL of 0.316 M Na2SO4 and 35.4 mL of 0.200 M KCl Na+ ______ M K+ _______M...

5 answers

##### In the Figure below; the power delivered to the 5 $ resistor equals Jmn Ma) 3.20 W 6) 4.00 W c) 1.92 W d) 0.64 W.ROn(u

In the Figure below; the power delivered to the 5 $ resistor equals Jmn M a) 3.20 W 6) 4.00 W c) 1.92 W d) 0.64 W. ROn (u...

5 answers

##### A? person's body mass index? (BMI) is computed bydividing the weight? (kg) by the square of height? (m).The accompanying table contains the BMI statistics for randomsamples of males and females. Assume that the two samples areindependent simple random samples selected from normallydistributed? populations, and do not assume that thepopulation standard deviations are equal. Let population 1 befemales. Complete parts? (a) through? (c) below.DATA SET:Female? BMI:n=71x=29.19s=7.45Male? BMI:n=77

A? person's body mass index? (BMI) is computed by dividing the weight? (kg) by the square of height? (m). The accompanying table contains the BMI statistics for random samples of males and females. Assume that the two samples are independent simple random samples selected from normally distribu...

5 answers

##### Como calcular as reacoes momento qual camga que esta ponte modelo sporta 12,95 20,18 20,6670 8 8 9 0 2,65675,6230

Como calcular as reacoes momento qual camga que esta ponte modelo sporta 12,95 20,18 20,6 670 8 8 9 0 2,65 67 5,62 30...