Now try Written Assignment. Question 1: Find all values of x, y and z that make the following matrix equation true, or demonstrate that no such values exist: 15 10

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Written Assignment Question 1? Please solve in details.
3:22 0 &
A 12%I
2.1 Matrix Operations sp 20.pdf
Example 3:
1
Given the matrices A = 3
7
3 -2 and B = , compute the products AB and BA, if they are
E . compute the products AB and BA, if they are
3.
defined.
Solutions:
[20 -191
• AB =-3
9
-9
• BA is undefined
Video Solution: http://youtu.be/cOFVIELyXuA?hd=1
Example 4:
Matrices A and B are said to commute if AB = BA.
Let A = 9. Find all matrices that commute with A.
Video Solution: https://youtu.be/zuxMQDUHFnl
Now try Written Assignment. Question 1:
Find all values of x, y and z that make the following matrix equation true, or demonstrate that no such
values exist:
3y 5
15 -39
-10
Theorem 2.1.2: Properties of Matrix Multiplication
Let A be an m xn matrix, and let B and C have sizes for which the indicated
sums and products are defined.
a. A(BC) = (AB)C
(associative law of multiplication)
b. A(B +C) = AB + AC
(left distributive law)
c. (B +C)A = BA + CA
d. r(AB) - (rA)B = A(rB)
for any scalar r
(right distributive law)
e. ImA = A = Al,
(identity for matrix multiplication)
III.
Transpose of a Matrix
DEFINITION: Transpose of a Matrix
Given an m x n matrix A, the transpose of A, denoted A", is defined to be an nxm matrix
created by rewriting the rows of A as columns.
Example 5:
Find the transnose of the matrix A =
! -3 71
II
Transcribed Image Text:3:22 0 & A 12%I 2.1 Matrix Operations sp 20.pdf Example 3: 1 Given the matrices A = 3 7 3 -2 and B = , compute the products AB and BA, if they are E . compute the products AB and BA, if they are 3. defined. Solutions: [20 -191 • AB =-3 9 -9 • BA is undefined Video Solution: http://youtu.be/cOFVIELyXuA?hd=1 Example 4: Matrices A and B are said to commute if AB = BA. Let A = 9. Find all matrices that commute with A. Video Solution: https://youtu.be/zuxMQDUHFnl Now try Written Assignment. Question 1: Find all values of x, y and z that make the following matrix equation true, or demonstrate that no such values exist: 3y 5 15 -39 -10 Theorem 2.1.2: Properties of Matrix Multiplication Let A be an m xn matrix, and let B and C have sizes for which the indicated sums and products are defined. a. A(BC) = (AB)C (associative law of multiplication) b. A(B +C) = AB + AC (left distributive law) c. (B +C)A = BA + CA d. r(AB) - (rA)B = A(rB) for any scalar r (right distributive law) e. ImA = A = Al, (identity for matrix multiplication) III. Transpose of a Matrix DEFINITION: Transpose of a Matrix Given an m x n matrix A, the transpose of A, denoted A", is defined to be an nxm matrix created by rewriting the rows of A as columns. Example 5: Find the transnose of the matrix A = ! -3 71 II
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