Q15 Problem 15.Determine which of the following sets are subspaces of R³?1.4r, 52,-27 z arbitrary number}V?2. {r, y, z-52+2y-82=-4)Yes3. (z.y. zz>0y20220}NoDetermine which of the following sets are subspaces of R¹1. The 3 x 3 matrices with integer entries2

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Answered: Problem 15. Determine which of the…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.5: Subspaces, Basis, Dimension, And Rank

Problem 10EQ

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Here is a data matrix for a line drawing: D=[012100002440] aDraw the image represented by D. bLet T=[1101]. Calculate the matrix product TD, and draw the image represented by this product. What is the effect of the transformation T? cExpress T as a product of a shear matrix and a reflection matrix. See Problem 2. 2. Verify that multiplication by the given matrix has the indicated effect when applied to the gray square in the table. Use c=3 in the expansion matrix and c=1 in the shear matrix. T1=[1001] Reflection in yaxis T2=[100c] Expansion or contraction in ydirection T3=[10c1] Shear in ydirection
Suppose masses m1, m2, m3, m4 are located at positions x1, x2, x3, x4 in a line and connected by springs with constants k12, k23, k34 whose natural lengths of extension are l12, l23, l34. Let f1, f2, f3, f4 denote the rightward forces on the masses, e.g., f1 = k12(x2 - x1 - l12). (a) Write the 4 x 4 matrix equation relating the column vectors f and x. Let K denote the matrix in this equation. (b) What are the dimensions of the entries of K in the physics sense (e.g., mass times tim, distance divided by mass, etc.)? (c) What are the dimensions of det(K), again in the physics sense? (d) Suppose K is given numerical values based on the unit meters, kilograms, and seconds. Now the system is rewritten with a matrix K' based on centimeters, grams, and seconds. What is the relationship of K' to K? What is the relationship of det(K') to det(K)?
I need help for problem (h). Check that the set at (h) is a subspace of Rn or not.
Below is the answers to problem 1 and 2, please help with problem 3. Problem 1 Use the svd() function in MATLAB to compute , the rank-1 approximation of . Clearly state what is, rounded to 4 decimal places. Also, compute the root-mean square error (RMSE) between and . Solution: %code %Define matrix A A = [1, 2, 3; 3, 3, 4; 5, 6, 7]; %Compute SVD of A [U, S, V] = svd(A); %Rank-1 approx A1 = U(:,1) * S(1,1) * V(:,1)'; RMSE = sqrt(mean((A(:) - A1(:)).^2)); %Display A1 rounded to 4 decimal places disp(round(A1, 4)); 1.7039 2.0313 2.4935 2.7243 3.2477 3.9867 4.9087 5.8517 7.1832 %Display RMSE disp(RMSE); 0.3257 Problem 2 Use the svd() function in MATLAB to compute , the rank-2 approximation of . Clearly state what is, rounded to 4 decimal places. Also, compute the root-mean square error (RMSE) between and . Which approximation is better, or ? Explain. Solution: %code A = [2, 4, 7; 3, 3, 5; 1, 6, 6]; % Compute SVD of A [U, S, V] = svd(A); % Rank-2…
Solve: (a) If a 7 x 9 matrix A has rank 5, what are the dimensions of the fourfundamental subspaces of A? (b) If a 3 x 4 matrix A has rank 3, what are the dimensions of R(A) and N(AT)?
2. Determine the exact distance between the two skew lines r1 = (3, 4, – 2) + s (1, – 1, 2), seR and r2 = (1, – 5, 3) + t (2, 3, 1), teR. using grade 12 knowloge no matrix
QUESTION 1Show that W = {(a, 0, b)|a, b ∈ R} is a subspace of R3
Suppose that S1 and S2 are subspaces of a vector space (V, F). Show that their intersection S1 ∩ S2 is also a subspace of (V, F). Is their union S1 ∪ S2 always a subspace?
the subset H={(x,y,z)∈ℝ³∣ 2x+3y-3z=4} it can be assured: * if u ∈H, v∈H , then u⊕v∈H* if u∈H, then c⊙u∈H, for all c∈R * H is a subspace of V=ℝ³ answer in each one if it is: False, true or cannot be established.
Problem 3: (2 marks) Let V = R be a vector space and let W be a subset of ', where W = {a,b,c):b = c² }. Determine, whether W is a subspace of vector space or not.
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Problem 15. Determine which of the following sets are subspaces of R³ ? V 1.4r, 52,-27 z arbitrary number} ? 2. {x, y, z-52+2y-82=-4) Yes 3. (z. y. 2 z 20 y 20:20}