Chapter 4: Q43. (page 200)

For which values of a, b, c, and d will $A = [\begin{matrix} a & b \\ c & d \end{matrix}] = A^{- 1}$ ?

Short Answer

Expert verified

The obtained values are $a = 1$ , $b = 0$ , $c = 1$ and $d = 0$ .

Step by step solution

Step 1- Determine the approach that can be used

The identity matrix $[\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$ can have the inverse that is also an identity matrix.

– Determine the value of a, b, c and d by using the approach

Use the obtained approach and determine the value of a, b, c and d.

The obtained values are $a = 1$ , $b = 0$ , $c = 1$ and $d = 0$ .

Step 3- Make the conclusion

As the inverse of an identity matrix $[\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$ will be $[\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$ so obtained values are correct.

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For which values of a, b, c, and d will $A = [\begin{matrix} a & b \\ c & d \end{matrix}] = A^{- 1}$ ?

Short Answer

Step by step solution

Step 1- Determine the approach that can be used

– Determine the value of a, b, c and d by using the approach

Step 3- Make the conclusion

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For which values of a, b, c, and d willA=abcd=A-1?

Short Answer

Step by step solution

Step 1- Determine the approach that can be used

– Determine the value of a, b, c and d by using the approach

Step 3- Make the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

For which values of a, b, c, and d will $A = [\begin{matrix} a & b \\ c & d \end{matrix}] = A^{- 1}$ ?