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If A is any square matrix of order 3 x 3 such that |adj. A| = 25 and |A| is non-positive, then the value of |A| is
We are given that A is a square matrix of order 3x3 and |adj(A)| = 25. We need to find the value of |A|. The formula for the relation between the determinant of a matrix A and its adjoint is given as under: |adj(A)| = |A|(n -1), where n is the order of the given matrix. When n = 3 for 3x3 matrix, itRead more
We are given that A is a square matrix of order 3×3 and |adj(A)| = 25. We need to find the value of |A|.
The formula for the relation between the determinant of a matrix A and its adjoint is given as under:
|adj(A)| = |A|(n -1), where n is the order of the given matrix.
When n = 3 for 3×3 matrix, it becomes:
|adj(A)| = |A|²
We are given that |adj(A)| = 25.
|A|² = 25
We find the square root of both sides of the equation
|A| = ±5
Since we know that |A| is non-positive we choose negative sign
|A| = -5
So, the correct answer is -5.
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If A is a square matrix such that |A| = 5, the value of |AAᵀ| is
A square matrix A |A| = 5 find |AA T| Theorem on Determinants for Matrix multiplication: |AB| = |A||B| AAᵀ For matrix multiplication. Then, using this theorem. |AA ᵀ |= |A|. |A|ᵀ| AṀ A being a square Matrix | AṀ ṀT|= |AT | Hence, |Aᵀ| = |A|. And we get; |AA T |= | A||A | = | A|² Since, the value ofRead more
A square matrix A |A| = 5 find |AA T|
Theorem on Determinants for Matrix multiplication:
|AB| = |A||B|
AAᵀ For matrix multiplication. Then, using this theorem. |AA ᵀ |= |A|. |A|ᵀ|
AṀ A being a square Matrix
| AṀ ṀT|= |AT |
Hence, |Aᵀ| = |A|.
And we get;
|AA T |= | A||A | = | A|²
Since, the value of A = 5
|AAᵀ| = 5² = 25
Therefore, the correct value of |AAᵀ| is 25.
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If A is any square matrix of order 3 x 3 such that |A| = 3, then the value of |adj. A| is
We are given that A is a square matrix of order 3x3 and |A| = 3. We have to find the value of |adj(A)|. The relation between the determinant of a matrix A and the determinant of its adjoint adj(A) is given by the formula: |adj(A)| = |A|^(n-1) Here, n = 3 because A is a 3x3 matrix. So the formula becRead more
We are given that A is a square matrix of order 3×3 and |A| = 3. We have to find the value of |adj(A)|.
The relation between the determinant of a matrix A and the determinant of its adjoint adj(A) is given by the formula:
|adj(A)| = |A|^(n-1)
Here, n = 3 because A is a 3×3 matrix. So the formula becomes:
|adj(A)| = |A|^(3-1) = |A|²
Since |A| = 3, we calculate:
|adj(A)| = 3² = 9
Hence, the correct value of |adj(A)| is 9.
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Which of the following is correct?
The determinant is the scalar computed from the elements of a square matrix. It supplies the crucial property of a matrix: it states whether a given matrix is invertible or not (in this case, nonzero determinant) and singular or degenerate (if it equals to zero). It is defined only for square matricRead more
The determinant is the scalar computed from the elements of a square matrix. It supplies the crucial property of a matrix: it states whether a given matrix is invertible or not (in this case, nonzero determinant) and singular or degenerate (if it equals to zero). It is defined only for square matrices (the number of rows and columns in these matrices is the same).
Determinant is a number attached to a square matrix.
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Given that A = [aᵢⱼ] is a square matrix of order 3 x 3 and |A| = -7, then the value of ∑³₁ ₌ ᵢ aᵢ₂ A ᵢ₂, where Aᵢⱼdemotes the cofactor of element a ᵢⱼis:
We are given that A is a square matrix of order 3x3 and |A| = -7. We are asked to find the value of the sum: ∑₁³ aᵢ₂ Aᵢ₂, where Aᵢ₂ denotes the cofactor of the element aᵢ₂. This sum corresponds to the determinant of matrix A when expanding along the second column. Specifically, the cofactor expansioRead more
We are given that A is a square matrix of order 3×3 and |A| = -7. We are asked to find the value of the sum:
∑₁³ aᵢ₂ Aᵢ₂, where Aᵢ₂ denotes the cofactor of the element aᵢ₂.
This sum corresponds to the determinant of matrix A when expanding along the second column. Specifically, the cofactor expansion formula for the determinant of a matrix A is:
|A| = ∑ᵢ aᵢⱼ Aᵢⱼ
where aᵢⱼ is the element of the matrix and Aᵢⱼ is its cofactor. Here, the expansion is along the second column. Thus, the sum becomes,
∑₁³ aᵢ₂ Aᵢ₂ = |A|
As we know that |A| = -7, therefore the value of the sum is -7.
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