Chapter 4: Q1. (page 171)

Determine whether the following statement is always, sometimes, or never true. Explain your reasoning.
For any matrix $A_{m \times n}$ for $m \neq n$ , $A^{2}$ is defined.

Short Answer

Expert verified

The provided statement will never be true.

Step by step solution

Step 1- Consider any values of m and n

Consider m as 1 and n as 2.

– Write the matrices with dimensions

Split the matrix . $A^{2}$

$A_{1 \times 2} \cdot A_{1 \times 2}$

As the inner dimensions are not the same which means that the matrix $A^{2}$ will not be defined.

Step 3- Write the conclusion

The provided statement will never be true due to same matrix and different count of row and columns.

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Determine whether the following statement is always, sometimes, or never true. Explain your reasoning.
For any matrix $A_{m \times n}$ for $m \neq n$ , $A^{2}$ is defined.

Short Answer

Step by step solution

Step 1- Consider any values of m and n

– Write the matrices with dimensions

Step 3- Write the conclusion

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Determine whether the following statement is always, sometimes, or never true. Explain your reasoning.For any matrixAm×nform≠n, A2is defined.

Short Answer

Step by step solution

Step 1- Consider any values of m and n

– Write the matrices with dimensions

Step 3- Write the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

Determine whether the following statement is always, sometimes, or never true. Explain your reasoning.
For any matrix $A_{m \times n}$ for $m \neq n$ , $A^{2}$ is defined.