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Question 3 1 point What is the value of p if the matrix A is a singular matrix? A=([3p,6],[-4,1]) 8 -8 4 -3

Question 33\newline11 point\newlineWhat is the value of p p if the matrix A A is a singular matrix?\newlineA=(3p6−41) A=\left(\begin{array}{ll} 3 p & 6 \\ -4 & 1 \end{array}\right) \newline88\newline−8 -8 \newline44\newline−3 -3

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Q. Question 33\newline11 point\newlineWhat is the value of p p if the matrix A A is a singular matrix?\newlineA=(3p6−41) A=\left(\begin{array}{ll} 3 p & 6 \\ -4 & 1 \end{array}\right) \newline88\newline−8 -8 \newline44\newline−3 -3
  1. Definition of Singular Matrix: A singular matrix is one that does not have an inverse, which means its determinant is 00.
  2. Calculate Determinant of Matrix A: Calculate the determinant of matrix A: det(A)=(3p)(1)−(−4)(6)\text{det}(A) = (3p)(1) - (-4)(6).
  3. Set Determinant Equal to 00: det(A)=3p+24\text{det}(A) = 3p + 24.
  4. Solve for pp: Set the determinant equal to 00 to find the value of pp: 3p+24=03p + 24 = 0.
  5. Final Value of p: Solve for pp: 3p=−243p = -24.
  6. Final Value of p: Solve for pp: 3p=−243p = -24.Divide both sides by 33 to get pp: p=−243p = -\frac{24}{3}.
  7. Final Value of pp: Solve for pp: 3p=−243p = -24.Divide both sides by 33 to get pp: p=−24/3p = -24 / 3.p=−8p = -8.

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