Find the value of k for A2 - kA - 14I = 0, if A = \(\begin{bmatrix}

1.	Find the value of k for A2 - kA - 14I = 0, if A = \(\begin{bmatrix} 2& 5 \\ 4 & 3 \end{bmatrix}\)1. -52. 53. 34. -3
Answer» Correct Answer - Option 2 : 5 Calculation: A² = A × A ⇒ A² = \(\begin{bmatrix} 2& 5 \\ 4 & 3 \end{bmatrix}\) × \(\begin{bmatrix} 2& 5 \\ 4 & 3 \end{bmatrix}\) ⇒ A2 = \(\begin{bmatrix} 24& 25 \\ 20 & 29 \end{bmatrix}\) Given A satisfy the equation A2 - kA - 14I = 0 ⇒ \(\begin{bmatrix} 24& 25 \\ 20 & 29 \end{bmatrix}\) - k \(\begin{bmatrix} 2& 5 \\ 4 & 3 \end{bmatrix}\) - 14 \(\begin{bmatrix} 1& 0 \\ 0 & 1 \end{bmatrix}\) = \(\begin{bmatrix} 0& 0 \\ 0 & 0 \end{bmatrix}\) ⇒ \(\begin{bmatrix} 24-2k-14&25-5k\\20-4k&29-3k-14\end{bmatrix}\) = \(\begin{bmatrix} 0& 0 \\ 0 & 0 \end{bmatrix}\) ⇒ 25 - 5k = 0 ⇒ k = 5

Find the value of k for A2 - kA - 14I = 0, if A = \(\begin{bmatrix} 2& 5 \\ 4 & 3 \end{bmatrix}\)1. -52. 53. 34. -3

Answer» Correct Answer - Option 2 : 5

Calculation:

A² = A × A

⇒ A² = \(\begin{bmatrix} 2& 5 \\ 4 & 3 \end{bmatrix}\) × \(\begin{bmatrix} 2& 5 \\ 4 & 3 \end{bmatrix}\)

⇒ A2 = \(\begin{bmatrix} 24& 25 \\ 20 & 29 \end{bmatrix}\)

Given A satisfy the equation

A2 - kA - 14I = 0

⇒ \(\begin{bmatrix} 24& 25 \\ 20 & 29 \end{bmatrix}\) - k \(\begin{bmatrix} 2& 5 \\ 4 & 3 \end{bmatrix}\) - 14 \(\begin{bmatrix} 1& 0 \\ 0 & 1 \end{bmatrix}\) = \(\begin{bmatrix} 0& 0 \\ 0 & 0 \end{bmatrix}\)

⇒ \(\begin{bmatrix} 24-2k-14&25-5k\\20-4k&29-3k-14\end{bmatrix}\) = \(\begin{bmatrix} 0& 0 \\ 0 & 0 \end{bmatrix}\)

⇒ 25 - 5k = 0

⇒ k = 5

Discussion

No Comment Found

Related InterviewSolutions

Find the value of k for A2 - kA - 14I = 0, if A = \(\begin{bmatrix} 2& 5 \\ 4 & 3 \end{bmatrix}\)1. -52. 53. 34. -3
If the A = \(\begin{bmatrix} -1& 3 \\ 4 & -2 \end{bmatrix}\) satisfies equation A2 + 3A - 10I = 0, find A-1.1. \({1\over10}\begin{bmatrix} -2& -3 \\ 4 & 1 \end{bmatrix}\)2. \({1\over10}\begin{bmatrix} -2& 3 \\ 4 & -1 \end{bmatrix}\)3. \({1\over10}\begin{bmatrix} 2& 3 \\ 4 & 1 \end{bmatrix}\)4. \({1\over10}\begin{bmatrix} 2& -3 \\ -4 & 1 \end{bmatrix}\)
If \(\begin{bmatrix} 1 & -4 & 3 \\\ 0 & 6 & -7 \\\ 2 & 4 & λ \end{bmatrix}\) is not an invertible matrix, then what is the value of λ ?
If \(\begin{bmatrix} 1 & -3 & 2 \\\ 2 & -8 & 5 \\\ 4 & 2 & λ \end{bmatrix}\) is not an invertible matrix, then what is the value of λ ?1. -12. 03. 14. 2
Let \(\Delta = \begin{vmatrix} Ax & x^2 & 1 \\\ By & y^2 & 1 \\\ Cz & z^2 & 1 \end{vmatrix}\) and \(\Delta_1 = \begin{vmatrix} A & B & C \\\ x & y & z \\\ zy & zx & xy \end{vmatrix}\), then1. Δ1 = -Δ 2. Δ1 ≠ Δ3. Δ1 - Δ = 04. Δ1 = Δ = 0
A square matrix A satisfies A2=I-A , where I is the identity matrix. If An =5A - 3I, find the value of n.
The inverse of the matrix \(\rm \begin{bmatrix} 2+3i & -i\\ i & 2-3i \end{bmatrix}\)is1. \( \frac{1}{12}\begin{bmatrix} 2-3i & i\\ -i & -2+3i \end{bmatrix}\)2. \( \frac{1}{12}\begin{bmatrix} 2-3i & i\\ -i & 2+3i \end{bmatrix}\)3. \( \frac{1}{12}\begin{bmatrix} 2+3i & i\\ -i & 2-3i \end{bmatrix}\)4. \( \frac{1}{12}\begin{bmatrix} 2-3i & -i\\ i & 2+3i \end{bmatrix}\)
Consider the following statements:1. If A′ = A; then A is a singular matrix, where A′ is the transpose of A.2. If A is a square matrix such that A3 = I, then A is non-singular.Which of the statements given above is/are correct ?1. 1 only 2. 2 only 3. Both 1 and 24. Neither 1 nor 2
Consider the following statements in respect of a square matrix A and its transpose AT :1. A + AT is always symmetric.2. A - AT is always anti-symmetric.Which of the statements given above is / are correct?1. 1 only2. 2 only3. Both 1 and 24. Neither 1 nor 2
If A and B are symmetric matrices of the same order, then (AB' - BA') is:1. Skew symmetric matrix2. Symmetric matrix3. Null matrix4. Identity matrix