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 2021-02-13 Answered

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

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Expert Answer

Aniqa O'Neill
Answered 2021-02-14 Author has 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.

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Jeffrey Jordon
Answered 2022-01-29 Author has 2064 answers

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