Matrices III Lowersixth Science Further Mathematics

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Challenge on matrices in SMF for Cameroon students.

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YAKILI LMS

Cameroon

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Matrices III Lowersixth Science Further Mathematics


Froggy Jumps Matrices III Lowersixth Science Further MathematicsOnline version Challenge on matrices in SMF for Cameroon students. by YAKILI LMS 1 A square matrix A is skew-symmetric if A^T = ? a A b A^−1 c −A 2 If A is skew-symmetric, what is a_ii for all i? a 1 b 0 c 2 3 Which is true for skew-symmetric 2x2 matrix [[0, a], [-a, 0]]? a Eigenvalues are both 1 b Trace is 0 c Determinant is 0 4 If A is skew-symmetric, A^T = ? a A^2 b −A c A 5 Which operation preserves skew-symmetry in a product AB? a If A and B are skew-symmetric, AB is skew-symmetric only if AB = BA b AB is always skew-symmetric c AB is always symmetric 6 An orthogonal matrix Q satisfies Q^T Q = ? a I b Q c 0 7 If Q is orthogonal, its inverse is what? a −Q^T b Q^T c Q 8 Which property holds for orthogonal matrices? a Increase determinant b Change trace c Preserve Euclidean norm 9 Which is a consequence of Q^T Q = I? a Rows are orthonormal only b Determinant is zero c Columns are orthonormal 10 If Q is orthogonal, det(Q) is? a 0 b Any real number c ±1 11 For matrices, the sum A+B is defined as? a Subtract diagonals only b Multiply corresponding entries c Add components element-wise 12 Properties of matrix addition: (A+B)^T = ? a A^T + B^T b A^T B^T c AB^T + A^T B 13 Which is true for matrix addition? a AB = BA always b AB ≠ BA in general c AB is always zero 14 Which is true if A is m×n and B is n×p? a A+B is defined for any sizes b A+B is zero matrix c A+B is defined only if m=n=p 15 Matrix addition is commutative: A+B = ? a AB b B+A c A−B 16 Scalar multiplication of a matrix: cA means? a Multiply rows by c b Multiply columns by c c Multiply every entry by c 17 Which is true for scalar multiplication and transpose? a c^T A^T = A^T b cA^T = A^T c (cA)^T = cA^T 18 If A is m×n and c is scalar, then cA is? a 1×1 b n×m c m×n 19 Which operation distributes over addition? a c(A+B) = cA + cB b (cA)(B) = c(AB) c A(B+C) = AB+AC 20 What is the result of A(B+C) with compatible sizes? a A^2 + B^2 + C^2 b A+BC c AB + AC 21 Which property holds for multiplication of matrices? a Distributivity over transpose b Associativity: (AB)C = A(BC) c Commutativity: AB = BA 22 If A is n×n and B is n×n, AB is? a n×n b 1×1 c m×p 23 Which is true about the zero matrix Z? a AZ = ZA = Z for any A b A does not exist c Z is never defined 24 Matrix multiplication is defined when? a Only for square matrices b Inner dimensions match c Outer dimensions match 25 If A is invertible and B is invertible, (AB)^−1 = ? a A^−1 B^−1 b A B c B^−1 A^−1 26 What is the determinant property for AB? a det(AB) = det(A)det(B) b det(AB) = det(A) + det(B) c det(AB) = det(A+B) 27 If A is orthogonal, then A^−1 equals? a A^T b −A c A 28 Which statement about orthogonal matrices is true? a They always have positive determinant b They preserve lengths and angles c They are always symmetric 29 Which property is preserved by scalar multiplication? a Non-commutativity b Nonlinearity c Linearity in addition 30 Which is not a property of matrix addition? a Associativity b Non-commutativity c Identity with zero matrix 31 Which operation distributes over scalar multiplication? a (cA)B = c(AB) b c(A+B) = cA + cB c A(B+C) = AB+AC? 32 If A and B are both skew-symmetric, what is (A+B)^T? a −(A+B) b A−B c A+B 33 Which is true for the trace of a skew-symmetric matrix? a Trace is zero b Trace equals determinant c Trace is nonzero 34 Which is true about orthogonal matrix columns? a They are linearly dependent b They are identical c They are orthonormal 35 Which operation preserves the identity of a square matrix? a Transposing twice b Multiplying by zero c Adding the zero matrix 36 If A is m×n and B is n×p, AB is? a n×n b m×p c p×m 37 Which statement is true for scalar multiple and transpose? a (cA)^T = cA^T b c^T A^T = A^T c cA^T ≠ A^T 38 Which property is not generally true for matrix addition? a A+(B+C) = (A+B)+C b A+B is commutative c AB = BA in general 39 An orthogonal matrix Q has determinant? a 0 b Any real number c ±1 40 What is a skew-symmetric matrix A characterized by? a A^T = -A b A^T = A c A = -A^T only on diagonal 41 Which is true for a skew-symmetric matrix regarding its diagonal? a Determinant is zero b All diagonal elements are zero c All rows are identical 42 What defines an orthogonal matrix O? a O^T O = I b O^T = O c O O^T = 0 43 Which is a property of matrix addition? a A + B = B + A b A + B = A c A + B = AB 44 True statement about matrix multiplication? a AB = BA always b AB may not equal BA c AB = A+B 45 Which is a valid scalar multiplication property? a A(B) = c(A+B) b c(A+B) = cA + cB c cA + B = c(A+B) 46 If O is orthogonal, what is true about O's inverse? a O^{-1} = I b O^{-1} = O^T c O^{-1} = O 47 Determinant of an orthogonal matrix is always a 2 b ±1 c 0 48 Two matrices can be added only if they have a Same determinant b Same number of rows c The same dimensions 49 What is (AB)^T equal to? a B^T A^T b A^T B^T A^T c A^T B^T 50 Scalar and matrix: (ab)A equals a a(bA) b aA + bA c A(ab)

Matrices III Lowersixth Science Further Mathematics

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Matrices III Lowersixth Science Further MathematicsOnline version

by YAKILI LMS

A square matrix A is skew-symmetric if A^T = ?

If A is skew-symmetric, what is a_ii for all i?

Which is true for skew-symmetric 2x2 matrix [[0, a], [-a, 0]]?

If A is skew-symmetric, A^T = ?

Which operation preserves skew-symmetry in a product AB?

An orthogonal matrix Q satisfies Q^T Q = ?

If Q is orthogonal, its inverse is what?

Which property holds for orthogonal matrices?

Which is a consequence of Q^T Q = I?

If Q is orthogonal, det(Q) is?

For matrices, the sum A+B is defined as?

Properties of matrix addition: (A+B)^T = ?

Which is true for matrix addition?

Which is true if A is m×n and B is n×p?

Matrix addition is commutative: A+B = ?

Scalar multiplication of a matrix: cA means?

Which is true for scalar multiplication and transpose?

If A is m×n and c is scalar, then cA is?

Which operation distributes over addition?

What is the result of A(B+C) with compatible sizes?

Which property holds for multiplication of matrices?

If A is n×n and B is n×n, AB is?

Which is true about the zero matrix Z?

Matrix multiplication is defined when?

If A is invertible and B is invertible, (AB)^−1 = ?

What is the determinant property for AB?

If A is orthogonal, then A^−1 equals?

Which statement about orthogonal matrices is true?

Which property is preserved by scalar multiplication?

Which is not a property of matrix addition?

Which operation distributes over scalar multiplication?

If A and B are both skew-symmetric, what is (A+B)^T?

Which is true for the trace of a skew-symmetric matrix?

Which is true about orthogonal matrix columns?

Which operation preserves the identity of a square matrix?

If A is m×n and B is n×p, AB is?

Which statement is true for scalar multiple and transpose?

Which property is not generally true for matrix addition?

An orthogonal matrix Q has determinant?

What is a skew-symmetric matrix A characterized by?

Which is true for a skew-symmetric matrix regarding its diagonal?

What defines an orthogonal matrix O?

Which is a property of matrix addition?

True statement about matrix multiplication?

Which is a valid scalar multiplication property?

If O is orthogonal, what is true about O's inverse?

Determinant of an orthogonal matrix is always

Two matrices can be added only if they have

What is (AB)^T equal to?

Scalar and matrix: (ab)A equals