1. Let a,b,c,d be row vectors and form the matrix A whose rows
are a,b,c,d. If...
1. Let a,b,c,d be row vectors and form the matrix A whose rows
are a,b,c,d. If by a sequence of row operations applied to A we
reach a matrix whose last row is 0 (all entries are 0) then:
a. a,b,c,d are linearly dependent
b. one of a,b,c,d must be 0.
c. {a,b,c,d} is linearly independent.
d. {a,b,c,d} is a basis.
2. Suppose a, b, c, d are vectors in R4 . Then they form a...
Let M be an n x n matrix with each entry equal to either 0 or...
Let M be an n x n matrix with each entry equal to either 0 or 1.
Let mij denote the entry in row i and column j. A
diagonal entry is one of the form mii for some i.
Swapping rows i and j of the matrix M denotes the following
action: we swap the values mik and mjk for k
= 1,2, ... , n. Swapping two columns is defined analogously.
We say that M is rearrangeable if...
This is a TRUE-FALSE Question with justification.
If Q is an orthogonal n×n matrix, then Row(Q)...
This is a TRUE-FALSE Question with justification.
If Q is an orthogonal n×n matrix, then Row(Q) =
Col(Q).
The Answer to this is TRUE. I want to know a solid
reasoning/explanation for it.
In one of the answers, it says that " Since Q is orthogonal,
QTQ = I, so Q is invertible, hence Row(Q) = Col(Q) =
Rn. But my question is: Why is it that for an invertible
matrix, Row(Q) = Col (Q) ?
Any other explanation that...