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Geetanjali Manish Natarajan

Asked: 3 years agoIn: Matrices

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

Jyoti Mukul Sane

Asked: 3 years agoIn: Matrices

A square matrix A satisfies A²=I-A , where I is the identity matrix. If Aⁿ =5A – 3I, find the value of n.

Akhila Saurabh Swamy

Asked: 3 years agoIn: Matrices

If the matrix \(\rm A = \left [ \begin{array}{cc} \alpha & \beta \\ \beta & \alpha \end{array}\right ]\) is such that A² = I, then which one of the following is correct?
1. α = 0, β = 1 OR α = 1, β = 0
2. α = 1, β = 1 OR α = 1, β = 0
3. α ≠ 1, β = 0
4. α = β = 0

Aarif Bhargava

Asked: 3 years agoIn: Matrices

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 ?

Neerendra Singh Taneja

Asked: 3 years agoIn: Matrices

Find the (adj A), if
A = \(\rm \begin{bmatrix} 3& 7& 1 \\ 2& 1& 8\\ 4& 5& 0\end{bmatrix}\)

1. \(\rm \begin{bmatrix} -40& 32& 55 \\ 5& -4& 13\\ 55& -22& -11\end{bmatrix}\)
2. \(\rm \begin{bmatrix} 3& 7& 1 \\ 2& 1& 8\\ 4& 5& 0\end{bmatrix}\)
3. \(\rm \begin{bmatrix} -40& 32& 6 \\ 5& -4& 13\\ 55& -22& -11\end{bmatrix}\)
4. \(\rm \begin{bmatrix} -40& 5& 55\\ 32& -4& -22\\ 6& 13& -11\end{bmatrix}\)

Ruchi Brahmbhatt

Asked: 3 years agoIn: Matrices

Consider the following statements in respect of a square matrix A and its transpose A^T :
1. A + A^T is always symmetric.
2. A – A^T is always anti-symmetric.
Which of the statements given above is / are correct?

1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2

Labeen Chandra Varma

Asked: 3 years agoIn: Matrices

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. \({1\over10}\begin{bmatrix} 2& -3 \\ -4 & 1 \end{bmatrix}\)

Mukund Rajagopal

Asked: 3 years agoIn: Matrices

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 2
4. Neither 1 nor 2

Arun Bhatti

Asked: 3 years agoIn: Matrices

The rank of Matrix \(A =\left[ {\begin{array}{*{20}{c}} 1&0&0&0&1\\ 0&1&1&1&0\\ 0&1&1&1&0\\ 0&1&1&1&0\\ 1&0&0&0&1 \end{array}} \right]\) is _______.
1. 2
2. 3
3. 4
4. 5

Vaishali Harpreet Lal

Asked: 3 years agoIn: Matrices

Let \(\Delta = \begin{vmatrix} Ax & x^2 & 1 \\\ By & y^2 & 1 \\\ Cz & z^2 & 1 \end{vmatrix}\) and \(\Delta_1 = \begin{vmatrix} A & B & C \\\ x & y & z \\\ zy & zx & xy \end{vmatrix}\), then
1. Δ₁ = -Δ
2. Δ₁ ≠ Δ
3. Δ₁ – Δ = 0
4. Δ₁ = Δ = 0

Load More Questions

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

A square matrix A satisfies A²=I-A , where I is the identity matrix. If Aⁿ =5A – 3I, find the value of n.

If the matrix \(\rm A = \left [ \begin{array}{cc} \alpha & \beta \\ \beta & \alpha \end{array}\right ]\) is such that A² = I, then which one of the following is correct?
1. α = 0, β = 1 OR α = 1, β = 0
2. α = 1, β = 1 OR α = 1, β = 0
3. α ≠ 1, β = 0
4. α = β = 0

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 ?

Consider the following statements in respect of a square matrix A and its transpose A^T :
1. A + A^T is always symmetric.
2. A – A^T is always anti-symmetric.
Which of the statements given above is / are correct?

1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2

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 2
4. Neither 1 nor 2

The rank of Matrix \(A =\left[ {\begin{array}{*{20}{c}} 1&0&0&0&1\\ 0&1&1&1&0\\ 0&1&1&1&0\\ 0&1&1&1&0\\ 1&0&0&0&1 \end{array}} \right]\) is _______.
1. 2
2. 3
3. 4
4. 5

Let \(\Delta = \begin{vmatrix} Ax & x^2 & 1 \\\ By & y^2 & 1 \\\ Cz & z^2 & 1 \end{vmatrix}\) and \(\Delta_1 = \begin{vmatrix} A & B & C \\\ x & y & z \\\ zy & zx & xy \end{vmatrix}\), then
1. Δ₁ = -Δ
2. Δ₁ ≠ Δ
3. Δ₁ – Δ = 0
4. Δ₁ = Δ = 0

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