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Chapter 2: Q17E (page 108)

TRUE OR FALSE?

Matrix [1236] is invertible.

Short Answer

Expert verified

The given statement is false.

Step by step solution

01

Invertible matrix

The matrix is said to be invertible if the determinant of that matrix is nonzero.

02

Compute the determinant of the matrix

Consider the matrix.

1236

The determinant of the matrix is,

det1236=1.6-2.3=0

As the determinant of the matrix is zero, thus, the matrix is not invertible.

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.

25. [2002]

In the example about the French coast guard in this section, suppose you are a spy watching the boat and listening in on the radio messages from the boat. You collect the following data:

鈥hen the actual position is [542],they radio [8952].

鈥hen the actual position is [641],they radio [8853].

Can you crack their code (i.e., find the coding matrix), assuming that the code is linear?

If A2 is invertible, then matrix A itself must be invertible.

If matrices A and B commute, then the formula A2B = BA2 must hold.

TRUE OR FALSE?

If the linear system A2x鈫�=b鈫� is consistent, then the systemrole="math" localid="1659352762883" Ax鈫�=b鈫� must be consistent as well.
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