Let the matrix X be
X=[−9 4
−7 k].

For X to have 0 as an eigenvalue, what must k be?

Question

Let the matrix X be
X=[−9	4
−7	k].

For X to have 0 as an eigenvalue, what must k be?

BlackTom AI · Accepted Answer

The question asks for the value of k such that the matrix X = [ [-9, 4], [-7, k] ] has 0 as an eigenvalue.

A matrix has 0 as an eigenvalue exactly when its determinant is zero, since det(X - 0I) = det(X).

Compute the determinant of X: det(X) = (-9)*k - (4)*(-7) = -9k + 28.

Setting the determinant equal to zero to ensure an eigenvalue of 0 gives the equation -9k + 28 = 0.

Solving for k involves isolating k: -9k = -28, so k = 28/9.

Note about the provided data: the answer options field was empty, so there is no listed set of choices to compare against. The essential steps involve recognizing the determinant condition for a zero eigenvalue, applying the determinant formula for a 2x2 matrix, and solving the resulting linear equation for k.

MATH1061/1002/1021 (ND) MATH1061 Canvas Quiz 9

Let the matrix X be X=[−9 4 −7 k]. For X to have 0 as an eigenvalue, what must k be?

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