Inverse Matrices and Solving Simultaneous Equations Using Matrices (VCE SSCE General Mathematics): Quizzes

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Inverse Matrices and Solving Simultaneous Equations Using Matrices
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What does A×A1A \times A^{-1} equal?

The identity matrix II

What is the 2×22 \times 2 identity matrix?

[1001]\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}

Which type of matrix can have an inverse?

Square matrices only

For matrix [abcd]\begin{bmatrix} a & b \\ c & d \end{bmatrix}, what is det(A)\text{det}(A)?

adbcad - bc

When does a matrix have no inverse?

When its determinant equals zero

Find det[3245]\text{det}\begin{bmatrix} 3 & 2 \\ 4 & 5 \end{bmatrix}.

77

In A×X=CA \times X = C, matrix AA contains what?

Coefficients of variables

To solve A×X=CA \times X = C, calculate:

X=A1×CX = A^{-1} \times C

Is A1×CA^{-1} \times C the same as C×A1C \times A^{-1}?

No, order matters in multiplication

How do you verify BB is the inverse of AA?

Calculate A×BA \times B and check if it equals II

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