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Chapter 6: Q46E (page 309)

There exists a real numberK such that the matrix[123456k789870065] is invertible.

Short Answer

Expert verified

Therefore,

k=3252and it isinvertible

So, the given statement is true.

Step by step solution

01

Matrix Definition

Matrix is a set of numbers arranged in rows and columns so as to form a rectangular array.

The numbers are called the elements, or entries, of the matrix.

If there are m rows and n columns, the matrix is said to be an 鈥�m by n鈥� matrix, written 鈥�m脳n .鈥�

02

Given

Given matrix,

A=123456k789870065

03

To check whether the given condition is true or false

We compute

detA=-6鈰�123567897+512356k898

role="math" localid="1659527820355" A=-6鈰�9+5鈰�(7k-41)A=35k-259.

So, for example,A is invertible for k=3252.

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Most popular questions from this chapter

25. If the determinant of a square matrix is -1, then Amust be an orthogonal matrix.

Consider two vectorsv鈬赌 and w鈬赌in鈩�3. Form the matrix A=[v鈬赌xw鈬赌v鈬赌w鈬赌] . Express detA in terms of||v鈬赌xw鈬赌||. For which choices of v鈬赌 and w鈬赌 is Ainvertible?

There exist invertible2脳2matrices A andBsuch thatdet(A+B)=detA+detB .

Use Cramer's rule to solve the systems in Exercises 22 through 24.

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The matrix [k214k-1-2111] is invertible for all positive constantsk.
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