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Chapter 2: Q60E (page 86)

In Exercises 55 through 64, find all matricesX that satisfy the given matrix equation.

1224X=l2

Short Answer

Expert verified

There is no such matrix X exists such that1224X=l2 .

Step by step solution

01

Assuming the matrix

Since the product of a matrix gives 2脳2matrix then the order of matrix X should be 2脳2

Let the matrix be. X=acbd.

We know the matrix I2=1001

Then the equation will become

1224acbd=1001

02

Solving the Matrix

To solve the given matrix equation, first multiply the left-hand side matrix.

a+2bc+2d2a+4d2c+4d=1001

Now, equating the left-hand and right-hand matrix.

a+2b=1c+2d=02a+4b=02c+4d=1

On solving the above equations, we will get 0=1, which is not possible for any value.

Hence, there is no such matrix that X exists such that1224X=I2

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Most popular questions from this chapter

In this exercise we will verify part (b) of Theorem 2.3.11 in the special case when A is the transition matrix [0.40.30.60.7]andx炉is the distribution vector[10]. [We will not be using parts (a) and (c) of Theorem 2.3.11]. The general proof of Theorem 2.3.11 runs along similar lines, as we will see in Chapter 7.

  1. ComputeA[12]andA[1-1]. WriteA[1-1]as a scalar multiple of the vector[1-1].
  2. Write the distribution vectorx鈫�=[10]as a linear combination of the vectors[12]and[1-1]
  3. Use your answers in part (a) and (b) to writeAx鈫�as a linear combination of the vectors[12]and[1-1]. More generally, write Amx鈫�as a linear combination of vectors[12]and[1-1], for any positive integer m. See Exercise 81.
  4. In your equation in part (c), let got to infinity to find limm鈫�鈭�Amx鈫�. Verify that your answer is the equilibrium distribution for A.

If matrix A is invertible, then matrix 5A must be invertible as well.

TRUE OR FALSE?

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

RUE OR FALSE?

The formula det(2A)=2det(A)holds for all 2脳2matrices A.

For which values of the constant k is the following matrix invertible?

[11112k14k2]
See all solutions

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