In this worksheet, we will practice checking whether a 2 × 2 matrix has an inverse and then finding its inverse, if possible.
Q1:
Is the matrix 31−31 invertible?
Q2:
Is the matrix 31−3−1 invertible?
Q3:
Are the matrices 1234,⎡⎢⎢⎣1121314⎤⎥⎥⎦ multiplicative inverses of each other?
Q4:
Find the multiplicative inverse of the matrix 𝐴=−4−1035, if possible.
Q5:
Given that the matrix 71−7𝑎 is invertible, what must be true of 𝑎.
Q6:
Find the set of real values of (𝑥) that make the matrix (𝑥)−382(𝑥)+3 singular.
Q7:
Consider the matrices 𝐴 and 𝐵. Determine (𝐴+𝐵)𝐴=−3−2−5−7,𝐵=−1289.
Q8:
Find the multiplicative inverse of 𝜃−𝜃𝜃𝜃.sincoscossin
Q9:
Given that 𝐴=𝑥−𝑥𝑦0𝑦, find 𝐴.
Q10:
Using matrix inverses, solve the following for 𝑋: 𝑋−324−3=0−230.
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