Master Matrix: The Cipher of Determinants

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A puzzle-adventure solving matrices mysteries

Créé par

AVIK GUPTA

India

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Froggy Jumps Master Matrix: The Cipher of DeterminantsVersion en ligne A puzzle-adventure solving matrices mysteries par AVIK GUPTA 1 Which operation is not defined for two matrices of incompatible inner dimensions (n×m and p×q)? a Scalar multiplication b Matrix addition c Matrix multiplication 2 If A is a 2×2 matrix with entries [a b; c d], which expression equals det(A)? a a d + b c b a + d c ad - bc 3 Which matrix is the transpose of [ [1,2,3], [4,5,6] ]? a [[1,2],[3,4]] b [[1,4],[2,5],[3,6]] c [[1,2],[3,4],[5,6]] 4 A square matrix A is symmetric if A^T = A. Which of the following is symmetric? a [[1,2],[3,4]] b [[0, 1],[2, 3]] c [[2, -1],[-1, 3]] 5 Determinant of a 3×3 matrix can be computed using which method? a Sarrus rule or cofactor expansion b Eigen decomposition only c Row reduction only 6 For a system Ax = b, if A is invertible, which method solves it directly? a x = A^{-1}b b x = Ab c x = A^T b 7 If A is 3×3 and det(A)=0, what can we say about A's inverse? a A^{-1} exists and is unique b A^{-1} does not exist c Det(A) nonzero 8 Which is true about the adjoint of A? a adj(A) satisfies A·adj(A) = det(A)·I b adj(A) has the same determinant as A c adj(A) = A^{-1} 9 Which of the following is a property of determinants? a det(AB)=det(A)det(B) b det(kA)=det(A)/k^3 for 3×3 A c det(A+B)=det(A)+det(B) 10 In the inverse-matrix method for solving Ax=b, what is x? a x = bA^{-1} b x = A^{-1}b c x = AA^{-1}b

Froggy Jumps

Master Matrix: The Cipher of DeterminantsVersion en ligne

A puzzle-adventure solving matrices mysteries

par AVIK GUPTA

Which operation is not defined for two matrices of incompatible inner dimensions (n×m and p×q)?

Scalar multiplication

Matrix addition

Matrix multiplication

If A is a 2×2 matrix with entries [a b; c d], which expression equals det(A)?

a d + b c

a + d

ad - bc

Which matrix is the transpose of [ [1,2,3], [4,5,6] ]?

[[1,2],[3,4]]

[[1,4],[2,5],[3,6]]

[[1,2],[3,4],[5,6]]

A square matrix A is symmetric if A^T = A. Which of the following is symmetric?

[[1,2],[3,4]]

[[0, 1],[2, 3]]

[[2, -1],[-1, 3]]

Determinant of a 3×3 matrix can be computed using which method?

Sarrus rule or cofactor expansion

Eigen decomposition only

Row reduction only

For a system Ax = b, if A is invertible, which method solves it directly?

x = A^{-1}b

x = Ab

x = A^T b

If A is 3×3 and det(A)=0, what can we say about A's inverse?

A^{-1} exists and is unique

A^{-1} does not exist

Det(A) nonzero

Which is true about the adjoint of A?

adj(A) satisfies A·adj(A) = det(A)·I

adj(A) has the same determinant as A

adj(A) = A^{-1}

Which of the following is a property of determinants?

det(AB)=det(A)det(B)

det(kA)=det(A)/k^3 for 3×3 A

det(A+B)=det(A)+det(B)

In the inverse-matrix method for solving Ax=b, what is x?

x = bA^{-1}

x = A^{-1}b

x = AA^{-1}b

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Master Matrix: The Cipher of Determinants

Froggy Jumps

À propos de cette activité

Créé par

Téléchargez la version pour jouer sur papier

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Master Matrix: The Cipher of DeterminantsVersion en ligne

par AVIK GUPTA

Which operation is not defined for two matrices of incompatible inner dimensions (n×m and p×q)?

If A is a 2×2 matrix with entries [a b; c d], which expression equals det(A)?

Which matrix is the transpose of [ [1,2,3], [4,5,6] ]?

A square matrix A is symmetric if A^T = A. Which of the following is symmetric?

Determinant of a 3×3 matrix can be computed using which method?

For a system Ax = b, if A is invertible, which method solves it directly?

If A is 3×3 and det(A)=0, what can we say about A's inverse?

Which is true about the adjoint of A?

Which of the following is a property of determinants?

In the inverse-matrix method for solving Ax=b, what is x?

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