Matrices C and D are shown belowC=begin{bmatrix}2&1&0 0&3&40&2&1 end{bmatrix},D=begin{bmatrix}a & b&-0.4 0&-0.2&0.80&0.4&-0.6 end{bmatrix}What values of a and b will make the equation CD=I true?a)a=0.5 , b=0.1b)a=0.1 , b=0.5c)a=-0.5 , b=-0.1

Efan Halliday

Efan Halliday

Answered question

2021-02-13

Matrices C and D are shown below
C=[210034021],D=[ab0.400.20.800.40.6]
What values of a and b will make the equation CD=I true?
a)a=0.5 , b=0.1
b)a=0.1 , b=0.5
c)a=-0.5 , b=-0.1

Answer & Explanation

Aniqa O'Neill

Aniqa O'Neill

Skilled2021-02-14Added 100 answers

Step 1
The given matrices are,
C=[210034021] and D=[ab0.400.20.800.40.6]
Step 2
Now multiply the matrices C and D as shown below.
CD=[210034021][ab0.400.20.800.40.6]
=[2a+0+02b0.2+00.8+0.8+00+0+000.6+1.60+2.42.40+0+000.4+0.40+1.60.6]
=[2a2b0.20010001]
Step 3
Now equate the matrix CD to the identity matrix I and obtain the values of a and b as follows.
CD=I
[2a2b0.20010001]=[100010001]
Two matrices are equal , only if the corresponding elements are equal.
2a=1
a=0.5
and
2b0.2=0
b=0.1
Step 4
Therefore, the CD = I is true for a = 0.5 and b =0.1.

Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-29Added 2605 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?