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Chapter 2: Q53E (page 109)

TRUE OR FALSE?

There exists an invertible10脳10 matrix that has 92ones among its entries.

Short Answer

Expert verified

The statement is false.

Step by step solution

01

Consider the parameters

A matrix will be non-invertible if it has identical rows.

An inverse of a matrix has an order, 10脳10

The number of ones in inverse matrix, 92

A matrix will have 100 entries. If 92 among them are ones, then, there will be identical rows. Such identical rows cancel out each other. Then, the inverse of that matrix will not exist.

02

Conclusion

Hence, the given statement is false.

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Most popular questions from this chapter

Consider the circular face in the accompanying figure. For each of the matrices A in Exercises 24 through 30, draw a sketch showing the effect of the linear transformation T(x)鈫�=Ax鈫�on this face.

27.[100-1]

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22.[100-1]

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