Matrices II Lowersixth Science Mathematics

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Matrices II Lowersixth Science Mathematics


Froggy Jumps Matrices II Lowersixth Science MathematicsOnline version Quick matrix problems by YAKILI LMS 1 What is the product of a 3x3 matrix with the same 3x3 matrix A and A? a A + A b A ÷ A c A × A 2 Which is the dimension of product AB if A is 3x3 and B is 3x3? a 3x3 b 3x2 c 2x3 3 If A is 3x3 and B is 3x3, what must be true for AB to be defined? a Both are symmetric b Inner dimensions match (3 = 3) c A is invertible 4 Which property is preserved by matrix multiplication? a Associativity b Distributivity over addition only c Commutativity 5 What is the transpose of a matrix A? a A^T with rows and columns swapped b Inverse of A c Determinant of A 6 If A is m×n, A^T is: a n×m b m×n c m×m 7 Which operation yields A × A^T for a square matrix A? a Gram-type product b Determinant c Inverse 8 Which is a property of the transpose? a (AB)^T = B^T A^T b A^T B^T = AB c (AB)^T = A^T B^T 9 What describes a symmetric matrix S? a S is diagonal only b S^T = -S c S^T = S 10 If S is symmetric, what is S^T? a S b Identity c -S 11 Which matrix equals its own transpose? a Skew-symmetric matrix b Symmetric matrix c Orthogonal matrix 12 Which statement is true for symmetric matrices? a They have A^T = A b They are always invertible c They have zero determinant 13 What is the transpose of a column vector v? a Row vector v^T b Zero vector c Same column vector 14 If A is 2x3, B is 3x4, AB is of size: a 3x4 b 2x3 c 2x4 15 What is the result of (A^T)^T? a A^2 b Inverse of A c A 16 Given A is symmetric, what is A^T? a -A b 0 c A 17 If A is 3x3 and B is 3x3, which is true? a Only AB is defined b Neither is defined c AB and BA are defined 18 Which product is defined for A(3x3) and B(3x3)? a Only BA b Only AB c AB and BA 19 The transpose of AB equals: a A B^T b B^T A^T c A^T B^T 20 What is the size of the transpose of a 4x6 matrix? a 4x4 b 4x6 c 6x4 21 Which describes a real symmetric matrix? a A^T = -A b A is orthogonal only c A^T = A and A is real 22 Which operation is not generally commutative? a Transposition b Addition c Matrix multiplication 23 For a 3x3 matrix A, what is det(A^T)? a det(A) b -det(A) c 0 24 Which is true for AB when A is m×n and B is n×p? a AB is m×p b AB is p×m c AB is n×n 25 Which property holds for transpose of a product? a (AB)^T = A B^T b (AB)^T = B^T A^T c (AB)^T = A^T B^T 26 A matrix that equals its own transpose is called: a Skew-symmetric b Symmetric c Orthogonal 27 If A is symmetric, det(A) is: a Zero b Always positive c Unchanged by transpose 28 The product AB is defined if: a A is invertible b The inner dimensions match c Both are symmetric 29 Which is a property of transpose? a det(A^T) = -det(A) b A^T = -A c (A^T)^T = A 30 What is A^T for a 1x4 row vector A? a 4x1 column vector b 1x4 row vector c Not defined 31 If A is 5x5, A^T is: a 5x5 b 5x4 c 4x5 32 Which is a correct property of symmetry? a A^T is inverse b A^T = A c A^T = -A 33 Which is true for any matrices A, B where AB is defined? a Only AB is defined b Transpose not related c AB and A^T B^T relation holds 34 What is the size of A^T if A is 6x2? a 6x2 b 3x4 c 2x6 35 If A is symmetric, which is true? a A^T = A b A^T = -A c A^T invertible only 36 Which of these is defined when A is 3x2 and B is 2x4? a AB is 3x2 b AB is 2x2 c AB is 3x4 37 What does (AB)^T equal? a A B^T b B^T A^T c A^T B^T 38 Which matrix remains the same when transposed? a Skew-symmetric b Orthogonal c Symmetric matrix 39 Transpose of a 0 matrix is: a Undefined b Non-zero c Still a 0 matrix 40 If A is symmetric and B is symmetric, AB is: a Always symmetric b Not necessarily symmetric c Never defined 41 The transpose of a sum is: a (A + B)^T = B^T A^T b (A + B)^T = A^T + B^T c A^T + B^T = AB 42 Given A is 3x3, B is 3x3, which is true? a Only BA defined b AB and BA defined; sizes 3x3 c Only AB defined 43 The product A^T A is: a Zero matrix b Gram matrix c Inverse 44 Which statement is false? a (AB)^T = B^T A^T b A^T A is symmetric c Matrix transpose always commutes with multiplication 45 If A is 2x3 and B is 3x2, AB is: a 2x2 b 2x3 c 3x3 46 A symmetric matrix is always: a Square b Diagonal only c Rectangular 47 Which operation gives a symmetric matrix from any A? a A^T A b A + A^T c A A^T 48 What is the dimension of A^T if A is m×n? a m×n b n×m c m×m 49 If A is symmetric, det(A^T) equals: a 0 b det(A) c -det(A) 50 Which is true about AB and BA when defined? a Always inverse b They are not generally equal c Always equal

Matrices II Lowersixth Science Mathematics

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Matrices II Lowersixth Science MathematicsOnline version

by YAKILI LMS

What is the product of a 3x3 matrix with the same 3x3 matrix A and A?

Which is the dimension of product AB if A is 3x3 and B is 3x3?

If A is 3x3 and B is 3x3, what must be true for AB to be defined?

Which property is preserved by matrix multiplication?

What is the transpose of a matrix A?

If A is m×n, A^T is:

Which operation yields A × A^T for a square matrix A?

Which is a property of the transpose?

What describes a symmetric matrix S?

If S is symmetric, what is S^T?

Which matrix equals its own transpose?

Which statement is true for symmetric matrices?

What is the transpose of a column vector v?

If A is 2x3, B is 3x4, AB is of size:

What is the result of (A^T)^T?

Given A is symmetric, what is A^T?

If A is 3x3 and B is 3x3, which is true?

Which product is defined for A(3x3) and B(3x3)?

The transpose of AB equals:

What is the size of the transpose of a 4x6 matrix?

Which describes a real symmetric matrix?

Which operation is not generally commutative?

For a 3x3 matrix A, what is det(A^T)?

Which is true for AB when A is m×n and B is n×p?

Which property holds for transpose of a product?

A matrix that equals its own transpose is called:

If A is symmetric, det(A) is:

The product AB is defined if:

Which is a property of transpose?

What is A^T for a 1x4 row vector A?

If A is 5x5, A^T is:

Which is a correct property of symmetry?

Which is true for any matrices A, B where AB is defined?

What is the size of A^T if A is 6x2?

If A is symmetric, which is true?

Which of these is defined when A is 3x2 and B is 2x4?

What does (AB)^T equal?

Which matrix remains the same when transposed?

Transpose of a 0 matrix is:

If A is symmetric and B is symmetric, AB is:

The transpose of a sum is:

Given A is 3x3, B is 3x3, which is true?

The product A^T A is:

Which statement is false?

If A is 2x3 and B is 3x2, AB is:

A symmetric matrix is always:

Which operation gives a symmetric matrix from any A?

What is the dimension of A^T if A is m×n?

If A is symmetric, det(A^T) equals:

Which is true about AB and BA when defined?