Basis =

impresijuzj
2021-11-28
Answered

Find a basis for the space of $2\times 2$ lower triangular matrices

Basis =

Basis =

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Thomas Conway

Answered 2021-11-29
Author has **10** answers

S = set of lower triangular matrices.

To find basis of s

Let

and

is linearly independent set

Finally answer:

Jeffrey Jordon

Answered 2022-01-30
Author has **2027** answers

Answer is given below (on video)

asked 2021-02-08

Let B be a 4x4 matrix to which we apply the following operations:

1. double column 1,

2. halve row 3,

3. add row 3 to row 1,

4. interchange columns 1 and 4,

5. subtract row 2 from each of the other rows,

6. replace column 4 by column 3,

7. delete column 1 (column dimension is reduced by 1).

(a) Write the result as a product of eight matrices.

(b) Write it again as a product of ABC (same B) of three matrices.

1. double column 1,

2. halve row 3,

3. add row 3 to row 1,

4. interchange columns 1 and 4,

5. subtract row 2 from each of the other rows,

6. replace column 4 by column 3,

7. delete column 1 (column dimension is reduced by 1).

(a) Write the result as a product of eight matrices.

(b) Write it again as a product of ABC (same B) of three matrices.

asked 2021-01-31

Find a basis for the space of $2\times 2$ diagonal matrices.

$\text{Basis}=\{\left[\begin{array}{cc}& \\ & \end{array}\right],\left[\begin{array}{cc}& \\ & \end{array}\right]\}$

asked 2021-12-20

Row equivalence. What is it exactly?

When matrices are row equivalent... why is this important? If a matrix like:

$$\left[\begin{array}{cc}1& 0\\ -1& 1\end{array}\right]$$

is row equivalent to the identity matrix (add 3 times the first row to the second), what does that mean exactly? Why is this a concept that we have to know as students of linear algebra? These matrices arent

When matrices are row equivalent... why is this important? If a matrix like:

is row equivalent to the identity matrix (add 3 times the first row to the second), what does that mean exactly? Why is this a concept that we have to know as students of linear algebra? These matrices arent

asked 2021-01-28

For each of the following matrices, determine a basis for each of the subspaces R(AT), N(A), R(A), and N(AT):

$A=\left[\begin{array}{cc}3& 4\\ 6& 8\end{array}\right]$

asked 2021-02-21

A,B,C are

1

-9

3

-1

9

asked 2021-02-19

If 4A-3B=2C (where A,B and C are all matrices) then Matrix A can be defined as:

Select one:

a) 0.5C+3B

b)$\frac{2C+3B}{4}$

c) 0.5C+0.75B

d) C+B

Select one:

a) 0.5C+3B

b)

c) 0.5C+0.75B

d) C+B

asked 2021-01-02

Suppose that A and B are diagonalizable matrices. Prove or disprove
that A is similar to B if and only if A and B are unitarily equivalent.