We have the equation of a square matrix A as A² - A + I = O Rearrange the equation to get A² - A = -I Now we factor the left-hand side, A(A - I) = -I To get the inverse of A (A⁻¹), multiply both sides of the equation by A⁻¹, A⁻¹ * A(A - I) = A⁻¹ * (-I) This gives us, (A - I) = -A⁻¹ Thus we can writeRead more
We have the equation of a square matrix A as
A² – A + I = O
Rearrange the equation to get
A² – A = -I
Now we factor the left-hand side,
A(A – I) = -I
To get the inverse of A (A⁻¹), multiply both sides of the equation by A⁻¹,
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
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
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
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.
If for a square matrix A, A² – A + I = O, then A⁻¹ equals
We have the equation of a square matrix A as A² - A + I = O Rearrange the equation to get A² - A = -I Now we factor the left-hand side, A(A - I) = -I To get the inverse of A (A⁻¹), multiply both sides of the equation by A⁻¹, A⁻¹ * A(A - I) = A⁻¹ * (-I) This gives us, (A - I) = -A⁻¹ Thus we can writeRead more
We have the equation of a square matrix A as
A² – A + I = O
Rearrange the equation to get
A² – A = -I
Now we factor the left-hand side,
A(A – I) = -I
To get the inverse of A (A⁻¹), multiply both sides of the equation by A⁻¹,
A⁻¹ * A(A – I) = A⁻¹ * (-I)
This gives us,
(A – I) = -A⁻¹
Thus we can write
A⁻¹ = I – A
Hence, the correct answer is option (c) I – A.
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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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