Explanation Let the general 2 × 3 matrices be A = [ a 11 a 12 a 13 a 21 a 22 a 23 ] , B = [ b 11 b 12 b 13 b 21 b 22 b 23 ] , and C = [ c 11 c 12 c 13 c 21 c 22 c 23 ] . Given that c and k are constants. Consider (a) in equation 3. A + B = B + A [ a 11 a 12 a 13 a 21 a 22 a 23 ] + [ b 11 b 12 b 13 b 21 b 22 b 23 ] = [ b 11 b 12 b 13 b 21 b 22 b 23 ] + [ a 11 a 12 a 13 a 21 a 22 a 23 ] [ a 11 + b 11 a 12 + b 12 a 13 + b 13 a 21 + b 21 a 22 + b 22 a 23 + b 23 ] = [ b 11 + a 11 b 12 + a 12 b 13 + a 13 b 21 + a 21 b 22 + a 22 b 23 + a 23 ] [ a 11 + b 11 a 12 + b 12 a 13 + b 13 a 21 + b 21 a 22 + b 22 a 23 + b 23 ] = [ a 11 + b 11 a 12 + b 12 a 13 + b 13 a 21 + b 21 a 22 + b 22 a 23 + b 23 ] Consider (b) in equation 3. ( A + B ) + C = A + ( B + C ) { [ a 11 a 12 a 13 a 21 a 22 a 23 ] + [ b 11 b 12 b 13 b 21 b 22 b 23 ] } + C = A + { [ b 11 b 12 b 13 b 21 b 22 b 23 ] + [ c 11 c 12 c 13 c 21 c 22 c 23 ] } [ a 11 + b 11 a 12 + b 12 a 13 + b 13 a 21 + b 21 a 22 + b 22 a 23 + b 23 ] + [ c 11 c 12 c 13 c 21 c 22 c 23 ] = [ a 11 a 12 a 13 a 21 a 22 a 23 ] + [ b 11 + c 11 b 12 + c 12 b 13 + c 13 b 21 + c 21 b 22 + c 22 b 23 + c 23 ] [ a 11 + b 11 + c 11 a 12 + b 12 + c 12 a 13 + b 13 + c 13 a 21 + b 21 + c 21 a 22 + b 22 + c 22 a 23 + b 23 + c 23 ] = [ a 11 + b 11 + c 11 a 12 + b 12 + c 12 a 13 + b 13 + c 13 a 21 + b 21 + c 21 a 22 + b 22 + c 22 a 23 + b 23 + c 23 ] Consider (c) in equation 3. A + 0 = A [ a 11 a 12 a 13 a 21 a 22 a 23 ] + [ 0 0 0 0 0 0 ] = [ a 11 a 12 a 13 a 21 a 22 a 23 ] [ a 11 a 12 a 13 a 21 a 22 a 23 ] = [ a 11 a 12 a 13 a 21 a 22 a 23 ] Consider (d) in equation 3. A + ( − A ) = 0 [ a 11 a 12 a 13 a 21 a 22 a 23 ] + { − [ a 11 a 12 a 13 a 21 a 22 a 23 ] } = [ 0 0 0 0 0 0 ] [ a 11 a 12 a 13 a 21 a 22 a 23 ] + [ − a 11 − a 12 − a 13 − a 21 − a 22 − a 23 ] = [ 0 0 0 0 0 0 ] [ a 11 − a 11 a 12 − a 12 a 13 − a 13 a 21 − 21 a 22 − a 22 a 23 − a 23 ] = [ 0 0 0 0 0 0 ] [ 0 0 0 0 0 0 ] = [ 0 0 0 0 0 0 ] Similarly, consider (a) in equation 4

10th Edition

ISBN: 9781119480150

Author: Kreyszig

Publisher: WILEY C

See similar textbooks

Videos

Question

Chapter 7.1, Problem 19P

To determine

To prove: The properties (3) and (4) for the general 2×3 matrix.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 7.1, Problem 18P

Chapter 7.1, Problem 20P

Students have asked these similar questions

/ Solve the equation Laplac transfoms:- wt = wxx WCX10) = 0 w (o,t) = f(t) lim w(x,t) = 0 X∞

Q/Find the Fourier sine and cosine transforms of f(x) = Xe-X

Q/solve the equation Laplac transforms:- x>0, to 43 1 иху u cx,α) = f(x) и a Cort ) = • lim u(x,t) = 0 8700 و X>0 , to

Chapter 7 Solutions

ADVANCED ENGINEERING MATH.>CUSTOM<

Ch. 7.1 - Equality. Give reasons why the five matrices in...Ch. 7.1 - Double subscript notation. If you write the matrix...Ch. 7.1 - Sizes. What sizes do the matrices in Examples 1,...Ch. 7.1 - Main diagonal. What is the main diagonal of A in...Ch. 7.1 - Scalar multiplication. If A in Example 2 shows the...Ch. 7.1 - If a 12 × 12 matrix A shows the distances between...Ch. 7.1 - Addition of vectors. Can you add: A row and a...Ch. 7.1 - Let Find the following expressions, indicating...Ch. 7.1 - Let Find the following expressions, indicating...Ch. 7.1 - Let Find the following expressions, indicating...

Knowledge Booster

$Advanced Math$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

To prove: The properties (3) and (4) for the general 2 × 3 matrix.

Videos

To prove: The properties (3) and (4) for the general 2×3 matrix.

Want to see the full answer?

Chapter 7 Solutions