Let A=begin{bmatrix}1 & 2&-1 1&0&31&1&-1 end{bmatrix} i) Find the determinant of A ii)Verify that the matrix begin{bmatrix}-frac{3}{4} & frac{1}{4}&frac{6}{4} 1&0&-1frac{1}{4}&frac{1}{4}&-frac{1}{2} end{bmatrix} is the inverse matrix of A

Reggie 2021-02-14 Answered
Let A=[121103111]
i) Find the determinant of A
ii)Verify that the matrix
[341464101141412] is the inverse matrix of A
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Expert Answer

jlo2niT
Answered 2021-02-15 Author has 96 answers
Step 1
For part (i) of a:
According to the given information, it is required to calculate the determinant of matrix
A=[121103111]
For this use the formula
|x1y1z1x2y2z2x3y3z3|=x1|y2z2y3z3|y1|x2z2x3z3|+z1|x2y2x3y3|
Step 2
Using above formula determinant of A can be calculated as
|A|=|121103111|
=1|0311|2|1311|1|1011|
=1(0×13×1)2(1×13×1)1(1×10×1)
=1(-3)-2(-1-3)-1
=-3+8-1
=4
Thus, determinant of matrix A is 4.
Step 3
For part (ii) of a:
To verify that the matrix
[341464101141412]
is inverse of given matrix A use the definition of identity matrix that states:
AA1=I
Step 4
Now calculate the multiplication of these two matrices, as
[121103111][341464101141412]=[1×34+2×11×141×14+2×01×141×64+2×11×121×34+0×1+3×141×14+0×0+3×141×64+0×1+3×121×34+1×11×141×14+1×01×141×64+1×11×12]
Jeffrey Jordon
Answered 2022-01-29 Author has 2064 answers

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