Let V = M22,W1(R) =a bb c2 V : a; b; c 2 RW2(R) =0 a?a 02 V : a 2 Rthen prove that W1 and W2 are subspaces of V, and nd the dimensionof W1, W2, and W1TW2 respectively. 10. Let V= M2×2;) = {% |b]EV: а, b, сERаW1 (R){[" ]аW2(R)E V : a E Rthen prove that W1 and W2 are subspaces of V, and find the dimensionof W1, W2, and W1NW2 respectively.

Answered: Image /qna-images/answer/e04d5444-6841-4c07-bc99-e2be02c26aea.jpg

Answered: 10. Let V = M2×2, W,(R) = {; ev : E V :…

10. Let V = M2×2, W,(R) = {; ev : E V : a, b, с€R = {[°. ] ev : « W2 (R) = V : a €R} then prove that W1 and W2 are subspaces of V, and find the dimension of W1, W2, and W1NW2 respectively.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

Let V = M22,
W1(R) =

a b
b c

2 V : a; b; c 2 R

W2(R) =

0 a
?a 0

2 V : a 2 R

then prove that W1 and W2 are subspaces of V, and nd the dimension
of W1, W2, and W1
T
W2 respectively.

10. Let V= M2×2;
) = {% |
b]
EV: а, b, сER
а
W1 (R)
{[" ]
а
W2(R)
E V : a E R
then prove that W1 and W2 are subspaces of V, and find the dimension
of W1, W2, and W1NW2 respectively.

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