If \(\begin{vmatrix}1&-1&x\\1&x&1\\x&-1&1\end{vmatrix}\) has no inverse, then the real value of \(x\) is
- 2
- 3
- 0
- 1
The Correct Option is D
Solution and Explanation
Has no inverse;
\(\Rightarrow|A|=0\)
\(x+1+1(1-x)+x\left(-1-x^{2}\right)=0\)
\(x+1+1-x-x-x^{3}=0\)
\(x^{3}-x-2=0\)
\(\Rightarrow x^{3}+2 x-x-2=0\)
\(\left(x^{2}-1\right)(x+2)=0\)
\(\Rightarrow x=\pm 1, x=-2\)
Real value of \(x=1\)
Top Questions on Transpose of a Matrix
- Let P be a square matrix such that P2 = I – P. For α, β, γ, δ ∈ N, if Pα + Pβ = γI – 29P and Pα – Pβ = δI – 13P, then α + β + γ – δ is equal to
- JEE Main - 2023
- Mathematics
- Transpose of a Matrix
- Let B =\(\begin{bmatrix} 1 & 3 & α \\ 1 & 2& 3 \\ α & α & 4 \end{bmatrix}\) , α>2 be the adjoint of a matrix A and |A| = 2, then [α - 2α α] B\(\begin{bmatrix} α \\ -2α \\ α \end{bmatrix}\)is equal to
- JEE Main - 2023
- Mathematics
- Transpose of a Matrix
- Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : For matrix A =\(\begin{bmatrix} 1 & 2 \\ 8 & 16 \end{bmatrix}\),rank of A = r(A) = 1
Reason R: For matrix A if |A| = 0, then it implies that rank of matrix A given by r(A) is less than full rank.
In the light of the above statements, choose the most appropriate answer from the options given below:- CUET (PG) - 2023
- Mathematics
- Transpose of a Matrix
- if A=\(\frac{1}{5! 6! 7!}\begin{bmatrix} 5! & 6! & 7!\\ 6! & 7! & 8! \\ 7! & 8! & 9! \end{bmatrix}\), then |adj(adj(2A))| is equal t
- JEE Main - 2023
- Mathematics
- Transpose of a Matrix
- Let Dk=\(\begin{vmatrix} 1 & 2k & 2k-1\\ n & n^2+n+2 & n^2 \\ n & n^2+n & n^2+n+2 \end{vmatrix} \) If \(∑^n_{k=1} D_k=96,\) The n is equal to
- JEE Main - 2023
- Mathematics
- Transpose of a Matrix
Questions Asked in BITSAT exam
- Two capacitors, of capacitance C, are connected in series. If one of them is filled with a dielectric substance K, what is the effective capacitance?
- BITSAT - 2023
- electrostatic potential and capacitance
- What is the dimension of the Gravitational constant?
- BITSAT - 2023
- Gravitation
- Minimum value of 5cos(2x) + 5sin(2x)
- BITSAT - 2023
- Trigonometric Functions
NaOH is deliquescent
- BITSAT - 2023
- States of matter
- The freezing point of the 0.05 molal solution of non - electrolyte in water is? (kf = 1.86)
- BITSAT - 2023
- Solutions
Concepts Used:
Transpose of a Matrix
The matrix acquired by interchanging the rows and columns of the parent matrix is called the Transpose matrix. The transpose matrix is also defined as - “A Matrix which is formed by transposing all the rows of a given matrix into columns and vice-versa.”
The transpose matrix of A is represented by A’. It can be better understood by the given example:
Now, in Matrix A, the number of rows was 4 and the number of columns was 3 but, on taking the transpose of A we acquired A’ having 3 rows and 4 columns. Consequently, the vertical Matrix gets converted into Horizontal Matrix.
Hence, we can say if the matrix before transposing was a vertical matrix, it will be transposed to a horizontal matrix and vice-versa.
Read More: Transpose of a Matrix
SUBSCRIBE TO OUR NEWS LETTER
