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Linear Algebra With Applications
Found in: Page 109
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

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Short Answer


There exists an invertible 10×10 matrix that has 92 ones among its entries.

The statement is false.

See the step by step solution

Step by Step Solution

Step 1: Consider the parameters

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

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

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.

Step 2: Conclusion

Hence, the given statement is false.

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