1)For all u, v E R^3, we have u . (u x v) = 0 2)For all vectors x, y E R^2, we have proj x = proj y? (x and y have a right arrow on top of them) 3)If there are more variables than equations in a...

1 answer below »

1)For all u, v E R^3, we have u . (u x v) = 0


2)For all vectors x, y E R^2, we have proj x = proj y? (x and y have a right arrow on top of them)


3)If there are more variables than equations in a system of linear equations, then there can NOT be a unique solution to the system?


4)If the m x n matrix A is a row equivalent to B, then Row (A)=Row (B)?


5)If A and B are uppertriangularmatrices, then A+B is an upper triangular matrix?


6)If A, B and C are all n x n matrices, and if AB=AC, then B=C?


7)If A is an invertible matrix, then rank (A ^-1)=1/rank(A)?


8)[1 0 2pi]



[0 1 0] is an elementary matrix?



[0 0 1]


9)Suppose that A is an n x n matrix and that B i obtained from a by adding r times the first row of A to the second row of A. Then det B= r det A?


10)Suppose that A is an invertible matrix. Then A^T is also invertible, and (A^T)^-1=(A^-1)^T?





Answered Same DayDec 22, 2021

Answer To: 1)For all u, v E R^3, we have u . (u x v) = 0 2)For all vectors x, y E R^2, we have proj x = proj y?...

David answered on Dec 22 2021
124 Votes
Solution

1)For all u, v E R^3, we have u . (u x v) = 0
Solution: True. As angle between u and
(u x v)= 90 degree.
2)For all vectors x, y E R^2, we have proj x = proj y? (x and y have a right arrow on top of
them)
Solution: False. If x and y are two different vectors then it may not be true.
3)If there are more variables than equations in a system of linear equations, then there can
NOT be a unique solution to the system?...
SOLUTION.PDF

Answer To This Question Is Available To Download

Related Questions & Answers

More Questions »

Submit New Assignment

Copy and Paste Your Assignment Here