Problem 1TFR: True-False Review For Questions a-g, decide if the given statement is true or false, and give a... Problem 2TFR: True-False Review For Questions a-g, decide if the given statement is true or false, and give a... Problem 3TFR: True-False Review For Questions a-g, decide if the given statement is true or false, and give a... Problem 5TFR: True-False Review For Questions a-g, decide if the given statement is true or false, and give a... Problem 6TFR Problem 7TFR Problem 1P: Use the standard inner product in 5 to determine the angle between the vectors v=(0,2,1,4,1) and... Problem 2P Problem 3P: If f(x)=sinx and g(x)=x on [0,], use the function inner product (5.1.5) to determine the angle... Problem 4P: If f(x)=sinx and g(x)=2cosx+4 on [0,/2], use the function inner product (5.1.5) to determine the... Problem 5P: Let m and n be positive real numbers. If f(x)=xm and g(x)=xn on an arbitrary interval [a,b], use the... Problem 6P: If v=(2+i,32i,4+i) and w=(1+i,13i,3i), use the standard inner product in 3 to determine, v,w, ||v||,... Problem 7P: If v=(63i,4,2+5i,3i) and w=(i,2i,3i,4i), use the standard inner product in 4 to determine, v,w,... Problem 8P: Let A=[a11a12a21a22] and B=[b11b12b21b22] be vectors in M2(R). Show that the mapping A,B=a11b11 does... Problem 9P: Referring to A and B in Problem 8, show that the mapping A,B=det(AB) does not define a valid inner... Problem 10P: Referring to A and B in Problem 8, show that the mapping A,B=a11b22+a12b21+a21b12+a22b11 does not... Problem 11P: Referring to A and B in Problem 8, show that the mapping A,B=a11b11+a12b12+a21b21+a22b22 5.1.13... Problem 12P: For Problems 1213, use the inner product (5.1.13) in Problem 11 to determine A,B, ||A||, and ||B||.... Problem 13P: For Problems 1213, use the inner product (5.1.13) in Problem 11 to determine A,B, ||A||, and ||B||.... Problem 14P: Let p1(x)=a+bx and p2(x)=c+dx be vectors in P1(R). Determine a mapping p1,p2 that defines an inner... Problem 15P: Let V=C0[0,1] and for f and g in V, consider the mapping f,g=01/2f(x)g(x)dx. Does this define a... Problem 16P: Let V=C0[0,1] and for f and g in V, consider the mapping f,g=01xf(x)g(x)dx. Does this define a valid... Problem 17P: Let V=C0[1,0] and for f and g in V, consider the mapping f,g=10xf(x)g(x)dx. Does this define a valid... Problem 18P: Consider the vector space R2. Define the mapping , by v,w=2v1w1+v1w2+v2w1+2v2w25.1.14 for all... Problem 19P: For Problems 1921, determine the inner product of the given vectors using a the inner product... Problem 20P: For Problems 1921, determine the inner product of the given vectors using a the inner product... Problem 21P: For Problems 1921, determine the inner product of the given vectors using a the inner product... Problem 22P Problem 23P Problem 24P Problem 25P Problem 26P Problem 27P Problem 28P Problem 29P Problem 30P Problem 31P Problem 32P Problem 33P Problem 34P Problem 35P Problem 36P Problem 37P format_list_bulleted