1. Consider the three vectors, u and v are 10 degrees above and below the x-axis...

1. Consider the three vectors, u and v are 10 degrees above and below the x-axis respectively, and ||u|| = 1, ||v|| = 2, and ||w|| = 3. Arrange the dot products taken among these vectors from least to greatest

2. Let A be a 4 x 6 matrix. Find the elimination matrix E that corresponds with the row operation "switch rows 1 and 3, and scale row 4 by a factor of 6.

3. Find the formula for the entry in the ith row and j column of the product AB in terms of the entries of A and B. Assume A is m x n and B is n x p.

Expert Solution

part(2) we have given that A is 4 by 6 matrix

suppose it looks like A=

we have to find the elimination matrix E by two operation that we have given are (i)switch rows 1 and 3(means you have to innterchange row 1 and 3)

(ii) scale row 4 by a factor of 6(multiply row 4 by 6)

then A=

part(3) here we have A is m by n matrix and B is n by p matrix

then AB will be an matrix of order m by p

then entries in the ith row=C_i₁ where i=1 to m for first column and where C_i1=A_inB_n1

C_i2 for second column and similarly C_ip for the p column

and formula for the column of the matrix=C_1i for first row where i= 1 to p

milcah answered 1 year ago

Suppose u, and v are vectors in R m, such that ∥u∥ = 1, ∥v∥ =...

Suppose u, and v are vectors in R m, such that ∥u∥ = 1, ∥v∥ = 4, ∥u + v∥ = 5. Find the inner product 〈u, v〉. Suppose {a1, · · · ak} are orthonormal vectors in R m. Show that {a1, · · · ak} is a linearly independent set.

Let u and v be vectors in R3. Consider the following statements.T or F (1) |u ...

Let u and v be vectors in R3. Consider the following statements.T or F (1) |u · v| ≤ ||u|| + ||v|| (2) If au + bv = cu + dv then a = c and b = d. (3) ||u + v||2 = ||u||2 + ||v||2 + 2(u · v) Let u, v, and w be vectors in R3. T or F. (1) u · v − ||u|| (2) (u · v) × w (3) || ( ||u|| projvu ...

For the following exercises, use the vectors shown to sketch u + v, u − v, and 2u.

For the following exercises, calculate u ⋅ v. Given the vectors shown in Figure 4, sketch u + v, u − v and 3v.

For the following exercises, calculate u ⋅ v.Given the vectors shown in Figure 4, sketch u + v, u − v and 3v.

Consider the utility functions of three individuals: u(x) = x1/2, v(x) = ln x, and h(x)...

Consider the utility functions of three individuals: u(x) = x1/2, v(x) = ln x, and h(x) = x – 0.01 x2, where x represents wealth. Consider also the following lotteries: X = (w0 + x1, w0 + x2, w0 + x3; ¼, ½, ¼ ) = (4, 16, 25; ¼, ½, ¼), where w0 = $2, and lottery Y in which w1 = $10, so that Y = (12, 24, 33; ¼, ½, ¼). Note that Y = X +...

show that for any two vectors u and v in an inner product space ||u+v||^2+||u-v||^2=2(||u||^2+||v||^2) give...

show that for any two vectors u and v in an inner product space ||u+v||^2+||u-v||^2=2(||u||^2+||v||^2) give a geometric interpretation of this result fot he vector space R^2

1. For this question, we define the following vectors: u = (1, 2), v = (−2,...

1. For this question, we define the following vectors: u = (1, 2), v = (−2, 3). (a) Sketch following vectors on the same set of axes. Make sure to label your axes with a scale. i. 2u ii. −v iii. u + 2v iv. A unit vector which is parallel to v (b) Let w be the vector satisfying u + v + w = 0 (0 is the zero vector). Draw a diagram showing the geometric relationship between...

2 Let u,v, and w be vectors, where u=(1,2,3,-1), v=(2,3,1,5) and w=(3,5,4,4). 2.1 Construct a basis...

2 Let u,v, and w be vectors, where u=(1,2,3,-1), v=(2,3,1,5) and w=(3,5,4,4). 2.1 Construct a basis for the vector space spanned by u, v and w. 2.2 Show that c=(1,3,2,1) is not in the vector space spanned by the above vectors u,v and w. 2.3 Show that d=(4,9,17,-11) is in the vector space spanned by the above vectors u,v and w, by expressing d as a linear combination of u,v and w.

Consider the linear transformation T which transforms vectors x C) in the y-axis. a) Express the...

Consider the linear transformation T which transforms vectors x C) in the y-axis. a) Express the vector X = T(x), the result of the linear transformation T on x in terms of the components x and y of X. by reflection [10 Marks] b) Find a matrix T such that T(x) = TX, using matrix multiplication. Calculate the matrix product T2 represent? Explain geometrically (or logically) why it should be this. c) T T . What linear transformation does this...

Find the angle θ between the vectors in radians and in degrees. u = cos π...

Find the angle θ between the vectors in radians and in degrees. u = cos π 3 i + sin π 3 j, v = cos 3π 4 i + sin 3π 4 j (a) radians (b) degrees

Question