Linear algebra with applications 2nd edition by holt test bank

Linear Algebra with Applications 2nd edition by Holt Test Bank Link full download solution manual: https://findtestbanks.com/download/linear-algebra-with-applications-2ndedition-by-holt-solution-manual/ Link full download test bank: https://findtestbanks.com/download/linearalgebra-with-applications-2nd-edition-by-holt-test-bank/ Chapter Euclidean Space 3u + v − 2w , 2.1 Vectors Determine where u= 1, v = Ans: , and w = 3 0 Express the given vector equation as a system of linear equations x x2 Ans : 3x + 2x = −2x =4 + 5x =1 Express the given vector equation as a system of linear equations 0x x 2x −x x3 = + 5x Ans: = −1 4x + 3x =2 5x + 7x =1 x + 2x − 3x =6 Express the given system of linear equations as a single vector equation −x + x =3 Ans: x1 Express2x+thex given−2x system=1 of linear equations as a single vector equation x 36 x 13 −x + x + x = 7x + 3x − x =1 x Ans: x 1 21 x 1= 3 11 The general solution to a linear system is given Express this solution as a linear combination of vectors x= − s x =s Ans: x1 =3 x s 1 The general solution to a linear system is given Express this solution as a linear combination of = 3−s x + 3s vectors x =s x =3+s x =s x1 Ans: x x s s x0 Find the unknowns in the given vector equation b = a Find a = 1, b = −1 26 Ans: the unknowns in the given vector equation a 3 = a c b Ans : a = 2, b = −1, c = 10 Express b as a linear combination of the other vectors, if possible a = ,a2 14 ,b= = 3a − 2a =b Ans: 11 Express b as a linear combination of the other vectors, if possible a =1 1 , a = 1, b = ,a = −2a + 2a +a =b 1 c(du + v) = (cd)u + v Ans : Fals e Ans: True or False: If u and v are vectors, and c and d are scalars, then Ans: False u v w 13 True or False: If , , and are vectors, then Ans: True 14 True or False: If u+v=w u − (v + w) = ( u − v) + (u − w) v=w−u , then 15 Sketch the graph of u = and v =, and then use the Parallelogram Rule to sketch the graph of u + v Ans: 16 Determine how to divide a total mass of 18 kg among the vectors u1 , u 0,u 3 2 so that the center of mass is 9 Ans: Place 10 kg at u1 , kg at u2 , and kg at u3 17 Find an example of a linear system with two equations and three variables that has x1 x x 3 s as the general solution +x x − 5x =5 Ans: A possible answer is x −x −x = −1 2.2 Span Find four vectors that are in the span of the given vectors u1 = = , u2 Ans: For example, 2, , 1 , and 2 Find five vectors that are in the span of the given vectors u1 = ,u2 = 1, u3 = 4, Ans: For example, , , , and 10 Determine if b is in the span of the other given vectors If so, write b as a linear combination of the other vectors a1 = 2, a = 3, b = 1 Ans: b = a −a Determine if b is in the span of the other given vectors If so, write b as a linear combination of the other vectors 1 a1 = , a = ,b= Ans: b is not in the span of a1 and a2 x +x − 2x =1 Find A , x , and b such that Ax = b corresponds to the given linear system −x + 2x + 4x =8 1 Ans: A= Findx −Ax, x =,and1 b x1 , x =x , and b = such that Ax = b corresponds to the given linear system 2x + 4x =3 0 x1 , x = x , and b = 1= −x + 5x Ans: A = x 1 05 Express the given system of linear equations as a vector equation −x 2x +x =1 x +2x + 4x Ans: x1 0− x x =0 x x 4 10 Determine if the columns of the given matrix span R 2 Ans: Yes, the columns span R Determine if the columns of the given matrix span R 1 Ans: No, the columns not span R 10 Determine if the system (where x and b have the appropriate number of components) has a solution for all choices of Ax = b b A= Ans: Yes, a solution exists 11 Find all values of h such that the vectors span R a1 = h , a2 = h Ans: All real numbers, except given vectors span 12 ? R For what value(s) of h the h ≠ ±2 2, h, Ans: All real numbers, except 13 True or False : Suppose a matrix A has nrows and m columns, with h≠5 Then the n columns of A not span R Ans: True 14 True or False: Suppose a matrix A has n rows and m columns, with columns of A span R n Ans: False Ans: True Then the m>n Ax = b b n 15 True or False: If the columns of a matrix A with n rows and m columns not span R , in R then there exists a vector n such that does not have a solution m≥ A n 16 True or False: If the columns of a matrix Ans: True 2.3 Linear Independence Determine if the given vectors are linearly independent 41 u= ,v= 2 Ans: Linearly independent Determine if the given vectors are linearly independent u= ,v= ,w= Ans: Not linearly independent Determine if the given vectors are linearly independent 0 u= ,v= ,w= n with n rows and m columns spans R , then Ans: Linearly independent Determine if the columns of the given matrix are linearly independent 3223 Ans: Linearly independent Determine if the columns of the given matrix are linearly independent 2 A= 2 32 Ans: Linearly independent Determine if the columns of the given matrix are linearly independent A= Ans: Not linearly independent Ax = Determine if the homogeneous system has any nontrivial solutions, where 31 A= 2 \ Ax = Ax Ans: has only the trivial solution Determine if the homogeneous system =0 has any nontrivial solutions, where A=0 1 1 Ax = Determine by inspection (that is, with only minimal calculations) if the given vectors form a linearly dependent or linearly independent set Justify your answer u= ,v= 20 ,w= Ans: Linearly dependent, by Theorem 2.14 10 Determine if one of the given vectors is in the span of the other vectors 2 u= ,v= ,w= Ans: Yes, since 11 Suppose matrix True or False: w = −u + v A has n rows and m columns, with Then the columns n