The matrix [math: [234x+1]] \left[\begin{array}{cc} 2&3 \ 4&x+1 \end{array} ight] will NOT have an inverse where:

Question

The matrix [math: [234x+1]] \left[\begin{array}{cc} 2&3 \ 4&x+1 \end{array}ight] will NOT have an inverse where:

BlackTom AI · Accepted Answer

The problem asks for the values of x for which the 2x2 matrix will not have an inverse, which happens precisely when its determinant is zero.
First, compute the determinant of the matrix [[2, 3], [4, x+1]]: det = 2*(x+1) − 3*4 = 2x + 2 − 12 = 2x − 10 = 2(x − 5).
A matrix is non-invertible when det = 0, so set 2(x − 5) = 0, which gives x = 5.
Thus, the matrix fails to have an inverse specifically at x = 5; at all other x-values, the determinant is nonzero and the matrix is invertible.
Option a. "x=5" correctly identifies the value that makes the determinant zero and thus the matrix non-invertible.
If there were other options, we could check them similarly by substituting into the determinant and determining whether det ≠ 0 or det = 0, but since no additional choices are provided, there is no further comparison to make here.

MCD1550 / MCD2140 - T3 - 2024 Test 3

The matrix [math: [234x+1]] \left[\begin{array}{cc} 2&3 \\ 4&x+1 \end{array}\right] will NOT have an inverse where:

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