Let

sagnuhh
2020-10-19
Answered

Let

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Ayesha Gomez

Answered 2020-10-20
Author has **104** answers

Let

Case 1: If $k=10, $ and since A satisfies its minial polynomial we have

Case 2: If k<10 then

In Any case we have

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 2021-02-25

Use the matrices AA and BB below instead of those in your text.

$A=\left[\begin{array}{cc}-6& -1\\ -3& -4\end{array}\right]B=\left[\begin{array}{cc}-1& 3\\ -5& -8\end{array}\right]$
1) 2A+B=?
2)A-4B=?

asked 2021-01-13

True or False - Determinants of two similar matrices are the same. Explain.

asked 2021-05-11

A matrix is defined as a rectangular array of numbers. Many of the arrays that you have worked have additional features, such as labels on the rows and columns or entries that are numbers with units. An array with additional features is technically not a matrix, instead we would call it a table. The difference between a matrix and a table is not vitally important in this unit, so we have worked with the underlying array of numbers and not worried about this technical detail. In more advanced courses in mathematics, like Linear Algebra, it will be important to be very precise about matrices. For now, describe and give examples of some of the ways a table can be different from a matrix. In your description and examples, be sure to include differences related to at least these three characteristics: entries, labels, and operations.

asked 2021-01-13

Determine which matrices are in reduced echelon form and which others are only in echelon form.

a)$\left[\begin{array}{cccc}1& 0& 1& 0\\ 0& 1& 1& 0\\ 0& 0& 0& 1\end{array}\right]$

b)$\left[\begin{array}{ccccc}0& 1& 1& 1& 1\\ 0& 0& 1& 1& 1\\ 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0\end{array}\right]$

c)$\left[\begin{array}{cccc}1& 5& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 1\end{array}\right]$
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a)

b)

c)

asked 2021-02-03

Detenninants of Sums Give an example of square matrices A and B for which $|A+B|\ne |A|+|B|$