Question

Let C = column matrix [1 2 3 1] and D = row matrix[−1 2 1 4] . Prove that (CD)^10 is the same as C(DC)^9D and do the calculation by hand.

Answer #1

Evaluate both the terms separately and then from the result obtained establish the equality.

Let Aequals=left bracket Start 2 By 2 Matrix 1st Row 1st Column
1 2nd Column 2 2nd Row 1st Column 8 2nd Column 18 EndMatrix right
bracket
1
2
8
18
, Bold b 1b1equals=left bracket Start 2 By 1
Matrix 1st Row 1st Column negative 5 2nd Row 1st Column negative 36
EndMatrix right bracket
−5
−36
, Bold b 2b2equals=left bracket Start 2 By 1
Matrix 1st Row 1st Column 3 2nd Row 1st Column 16 EndMatrix right...

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 R*= R\ {0} be the set of nonzero real
numbers. Let
G= {2x2 matrix: row 1(a b) row 2 (0 a) | a in
R*, b in R}
(a) Prove that G is a subgroup of GL(2,R)
(b) Prove that G is Abelian

. Given the matrix A =
1 1 3 -2
2 5 4 3
−1 2 1 3
(a) Find a basis for the row space of A
(b) Find a basis for the column space of A
(c) Find the nullity of A

1. Let A be the 2x2 matrix in M_{2x2}(C), whose first row is
(0,1) and second row is (-1,0).
(a) Show that A is normal.
(b) Find (complex) eigenvalues of A.
(c) Find an orthogonal basis for C^2, which consists of
eigenvectors of A.
(d) Find an orthonormal basis for C^2, which consists of
eigenvectors of A.

A=l
−2 −7 −45
4 5 27
1 3 20
.
Find the third column of
A−1 ( subscript -1)
without computing the other two columns.
How can the third column of
A−1 ( subscript -1)
be found without computing the other columns?
A.
Row reduce the augmented matrix [AI3( not 13 but capital I
subscript 3].
B.
Row reduce the augmented matrix [A e3],where e3 is the third
column of I3.( capital I subscript 3)
C.
Row reduce the...

Let T be an linear transformation from ℝr to ℝs. Let A be the
matrix associated to T.
Fill in the correct answer for each of the following situations
(enter your answers as A, B, or C).
1. Every row in the row-echelon
form of A has a leading entry.
2. Two rows in the row-echelon form of
A do not have leading entries.
3. The row-echelon form of A has a
leading entry in every column.
4. The row-echelon...

Consider the following matrix.
A =
4
-1
-1
2
6
-3
6
4
1
Let B = adj(A). Find b31,
b32, and b33. (i.e., find
the entries in the third row of the adjoint of A.)

Let M = ( (−3 1 3 4), (1 2 −1 −2), (−3 8 4 2))
14. (3 points) Let B1 be the basis for M you found by row
reducing M and let B2 be the basis for M you found by row reducing
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B1.

Let's say you have a 4 row, 7 column Matrix A that is linearly
dependent. How do you find a subset of A that is a basis for R4 and
why that set forms a basis for R4?

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