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Matrices C and D are shown below:
[tex]C=\left[\begin{array}{ccc}2&1&0\\0&3&4\\0&2&1\end{array}\right][/tex] [tex]D=\left[\begin{array}{ccc}a&b&-0.4\\0&-0.2&0.8\\0&0.4&-0.6\end{array}\right][/tex]
What values of a and b will make the equation CD = I true?
(i) a = 0.5
b = 0.1
(ii) a = 0.1
b = 0.5
(iii) a = -0.5
b = -0.1
Answer: (i) a = 0.5
b = 0.1
Step-by-step explanation: Identity Matrix (I) is a n x n square matrix with the number 1 on the main diagonal and 0 everywhere else.
The question asks for multiplication of matrices, i.e.:
[tex]\left[\begin{array}{ccc}2&1&0\\0&3&4\\0&2&1\end{array}\right][/tex] . [tex]\left[\begin{array}{ccc}a&b&-0.4\\0&-0.2&0.8\\0&0.4&-0.6\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right][/tex]
To multiply matrices, the number of columns of the 1st matrix must be the same as the number of rows of the 2nd.
Matrix C is a 3x3 square matrix and so is matrix D, so, values of a and b:
[tex]2a=1[/tex] [tex]2b-0.2=0[/tex]
[tex]a=\frac{1}{2}[/tex] [tex]2b=0.2[/tex]
a = 0.5 [tex]b=0.1[/tex]
For the equation CD=I be true, a and b has to be 0.5 and 0.1, respectively.
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