2 makeMatrix(randRange(-2, 5, DIM, DIM)) matrixDet(MAT)
makeMatrix([["a","b"],["c","d"]]) makeMatrix([["d","-b"],["-c","a"]]) matrixInverse(MAT) matrixPad(SOLN_MAT, 3, 3) printMatrix(function(a) { var sign = (a < 0) ? "-" : ""; var frac = toFraction(abs(a)); // omit denominator when it's equal to 1 if (frac[1] === 1) { return sign + frac[0]; } return sign + "\\frac{" + frac[0] + "}{" + frac[1] + "}"; }, SOLN_MAT) "\\textbf " + randFromArray("ABCDEF")

PRETTY_MAT_ID = printSimpleMatrix(MAT)

What is PRETTY_MAT_ID^{-1}?

elem elem

Express your answer in fractions or exact decimals.

The fractions do not need to be simplified.

PRETTY_MAT_ID^{-1} = \frac{1}{det(PRETTY_MAT_ID)}adj(PRETTY_MAT_ID)

Step 1: Find the adjugate

For any 2x2 matrix printSimpleMatrix(HINT_MAT), the adjugate is printSimpleMatrix(HINT_MAT_ADJ).

adj(PRETTY_MAT_ID) = printSimpleMatrix(matrixAdj(MAT), KhanUtil.BLUE)

Step 2: Find the determinant

For any 2x2 matrix printSimpleMatrix(HINT_MAT), the determinant is matrix2x2DetHint(HINT_MAT).

det(PRETTY_MAT_ID) = matrix2x2DetHint(MAT) = expr(["color", KhanUtil.RED, DET])

Step 3: Put it all together

Now that we have both the determinant and the adjugate, we can compute the inverse.

PRETTY_MAT_ID^{-1} = \frac{1}{expr(["color", KhanUtil.RED, DET])} printSimpleMatrix(matrixAdj(MAT), KhanUtil.BLUE)

= PRETTY_SOLN_MAT