Determine whether each of the following statements is true or false, and explain why.If A and B are square matrices of the same size, then

Tammy Todd
2021-02-19
Answered

Determine whether each of the following statements is true or false, and explain why.If A and B are square matrices of the same size, then

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asked 2021-01-31

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

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

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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.

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16. Give an example of a function from N to N that isa) one-to-one but not onto.b) onto but not one-to-one.c) both onto and one-to-one (but different from the identity function).d) neither one-to-one nor onto

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Let B be a matrix $m\times n$. Let $b\in {\mathbb{R}}^{m}$. Let $f:{\mathbb{R}}^{n}\to {\mathbb{R}}^{m}$ be the function defined as $f(x)=Bx+b$

What is the Df(x)(derivative) and how can I find it from the derivative definition?

What is the Df(x)(derivative) and how can I find it from the derivative definition?

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Prove that if B is symmetric, then $\Vert B\Vert $ is the largest eigenvalue of B.

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( 2x+3y =103x+4y=20

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Find $5\times 5$ invertible matrix A over ${\mathbb{F}}_{3}$ such that ${A}^{-1}=2{A}^{3}+2I$, $A\ne I$