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Chapter 6: Q13E (page 309)

Matrix[910037541008100987654100]is invertible.

Short Answer

Expert verified

Therefore, the given statement is true.

Step by step solution

01

Matrix Definition. 

Matrix is aset of numbers arranged in rows and columns so as to form a rectangulararray.

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,

[910037541008100987654100]

03

To check whether the given condition is true or false.

Given Matrix,

[910037541008100987654100]

First, we find determinant of the given matrix.

The determinant of the matrix isdetA=97763383 .

So, the matrix is invertible.

Therefore, the given statement is true.

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Most popular questions from this chapter

Consider the quadrilateral in the accompanying figure, with vertices Pi=(xi,yi), for i=1,2,3,4. Show that the area of this quadrilateral is

12(det[x1x2y1y2]+det[x2x3y2y3]+det[x3x4y3y4]+det[x4x1y4y1]).

Use Gaussian elimination to find the determinant of the matrices A in Exercises 1 through 10.

8. [0000210003010040010500016]

If all the columns of a square matrixAare unit vectors, then the determinant ofAmust be less than or equal to 1.

Show that an nxn matrixAhas at least one nonzero minor if (and only if) rank(A)鈮�n-1.

If is any noninvertible square matrix, then detA=det(rrefA).
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