Finding Inner Product, Length, and Distance In Exercises 29-32, find (a) 〈 A , B 〉 , (b) ‖ A ‖ , (c) ‖ B ‖ , and (d) d 〈 A , B 〉 for the matrices in M 2 , 2 using the inner product 〈 A , B 〉 = 2 a 1 1 b 1 1 + a 1 2 b 1 2 + a 2 1 b 2 1 + 2 a 2 2 b 2 2 . A = [ 1 0 0 − 1 ] , B = [ 1 1 0 − 1 ]
Finding Inner Product, Length, and Distance In Exercises 29-32, find (a) 〈 A , B 〉 , (b) ‖ A ‖ , (c) ‖ B ‖ , and (d) d 〈 A , B 〉 for the matrices in M 2 , 2 using the inner product 〈 A , B 〉 = 2 a 1 1 b 1 1 + a 1 2 b 1 2 + a 2 1 b 2 1 + 2 a 2 2 b 2 2 . A = [ 1 0 0 − 1 ] , B = [ 1 1 0 − 1 ]
Solution Summary: The author explains that the value of inner product langle A,Brangle is 1.
Finding Inner Product, Length, and DistanceIn Exercises 29-32, find (a)
〈
A
,
B
〉
, (b)
‖
A
‖
, (c)
‖
B
‖
, and (d)
d
〈
A
,
B
〉
for the matrices in
M
2
,
2
using the inner product
〈
A
,
B
〉
=
2
a
1
1
b
1
1
+
a
1
2
b
1
2
+
a
2
1
b
2
1
+
2
a
2
2
b
2
2
.
a) Is A diagonalizable? Explain.b) If A is diagonalizable, rewrite A as XDX-1 (explain the choice of matrices).c) if part (b) is possible, verify it by showing that A=XDX-1.
Let A and B be square matrices of order 3 such that ∣A∣ = 4 and ∣B∣ = 5.(a) Find ∣AB∣. (b) Find ∣2A∣.(c) Are A and B singular or nonsingular? Explain. (d) If A and B are nonsingular, find ∣A−1∣ and ∣B−1∣. (e) Find ∣(AB)T∣.
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Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY