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Problem 3

University of California - Los Angeles

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Problem 1

Two matrices are ________ if all of their corresponding entries are equal.

Answer

Equal.

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## Discussion

## Video Transcript

this question states that if we have two different matrices and, um, if their corresponding entries are equal, what would what can be classified the matrices as so just quickly give a brief recap. A matrix, of course, is something like, for example, if you have a one by two matrix a beat like such and we have a different one, let's say 11 and 12. And basically what this question states is that if a is equal to 11 and B is equal to 12 what can we say about these two matrices? So what can we say about these things is that these two Major sees there for equal to each other, and that would be the answer to this question here.

## Recommended Questions

Two matrices are _____ when they have the same dimension and all of their corresponding entries are equal.

Concept Check Two matrices are equal if they have the same ____ and if corresponding elements are ____.

In order to add two matrices, they must have the same _____.

Fill in the blanks.

For matrices $A$ and $B$ to be equal, they must be the same _____, and corresponding entries must be _____.

Equality of Matrices Determine whether the matrices $A$

and $B$ are equal.

$$

A=\left[ \begin{array}{rrr}{1} & {-2} & {0} \\ {\frac{1}{2}} & {6} & {0}\end{array}\right] \quad B=\left[ \begin{array}{rr}{1} & {-2} \\ {\frac{1}{2}} & {6}\end{array}\right]

$$

Equality of Matrices Determine whether the matrices A and B are equal.

$$

A=\left[\begin{array}{rrr}{1} & {-2} & {0} \\ {\frac{1}{2}} & {6} & {0}\end{array}\right] \quad B=\left[\begin{array}{rr}{1} & {-2} \\ {\frac{1}{2}} & {6}\end{array}\right]

$$

Determine whether the matrices in each pair are inverses of each other.$ $\left[\begin{array}{rr}3 & 1 \\ $$\left[\begin{array}{cc}

\frac{1}{2} & 0 \\

0 & \frac{1}{2}

\end{array}\right],\left[\begin{array}{ll}

2 & 0 \\

0 & 2

\end{array}\right]$$

Determine whether the two matrices in each pair are equal. Justify your reasoning.

$$

\left[\begin{array}{rr}{-2} & {3} \\ {5} & {0}\end{array}\right],\left[\begin{array}{cc}{2(-1)} & {2(1.5)} \\ {2(2.5)} & {2(0)}\end{array}\right]

$$

Equality of Matrices Determine whether the matrices $A$

and $B$ are equal.

$$

A=\left[ \begin{array}{cc}{\frac{1}{4}} & {\ln 1} \\ {2} & {3}\end{array}\right] \quad B=\left[ \begin{array}{cc}{0.25} & {0} \\ {\sqrt{4}} & {\frac{6}{2}}\end{array}\right]

$$

Equality of Matrices Determine whether the matrices A and B are equal.

$$

A=\left[\begin{array}{cc}{\frac{1}{4}} & {\ln 1} \\ {2} & {3}\end{array}\right] \quad B=\left[\begin{array}{cc}{0.25} & {0} \\ {\sqrt{4}} & {\frac{1}{2}}\end{array}\right]

$$