Matrices III Lowersixth Science Mathematics

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Matrices III Lowersixth Science Mathematics


Froggy Jumps Matrices III Lowersixth Science MathematicsVersión en línea Lowersixth science math: Matrix topics. por YAKILI LMS 1 What is a skew-symmetric matrix A? a A = -A^T b A^T = -A c A^T = A 2 Which property defines an orthogonal matrix Q? a Q Q^T = 0 b Q^T Q = I c Q^T Q = 0 3 If A and B are square, what is A + B? a Difference of A and B b Product of A and B c A new matrix with sums of corresponding entries 4 Which is true about matrix addition? a Not closed under addition b Commutative: A + B = B + A c Distributive over multiplication 5 What is the result of A + 0 for any matrix A? a A b I c 0 6 What must be true for matrix addition to be defined? a Same determinant b Same trace c Matrices have the same dimensions 7 Matrix multiplication is defined for? a Only square matrices b Any two matrices c A with B where inner dimensions match 8 What is the product of two diagonal matrices? a A zero matrix b A diagonal matrix with products of diagonal entries c A matrix with ones on diagonal 9 What is the identity matrix I? a Diagonal with ones; I^2 = I b All zeros c Diagonal with zeros 10 For a diagonal matrix D, what is D^2? a Diagonal with squared diagonal entries b Diagonal with reduced entries c Zero matrix 11 What is a unit matrix? a Null matrix b Another name for identity matrix c Diagonal with random values 12 Which property does the transpose operation preserve? a Determinant equality under transpose b Trace changes sign c Matrix order changes 13 What is the transpose of a row vector? a Scalar b Row vector c Column vector 14 Which operation is not commutative in general? a Addition b Scalar multiplication c Matrix multiplication 15 If A is skew-symmetric, what is A^T? a A^-1 b -A c A 16 A skew-symmetric matrix A has what property when size odd? a Determinant is nonzero b All entries are zero c Trace is zero 17 What is the determinant of an odd-order skew-symmetric matrix? a Zero b Undefined c Nonzero 18 How do you check orthogonality of Q? a Q^T Q = 0 b Q Q^T = 0 c Q^T Q = I 19 What is the effect of multiplying by the identity matrix? a Flips sign of entries b Increases rank c No change: A I = A 20 Which is true for matrix addition and scalar multiplication? a A + (BC) = (A+B)C b Distributive: a(A + B) = aA + aB c A+B = AB 21 If A is m x n and B is n x p, what is AB size? a m x p b m x n c n x p 22 What is the trace of a diagonal matrix? a Product of diagonal entries b Count of nonzero entries c Sum of diagonal entries 23 A diagonal matrix has what feature? a All off-diagonal entries are zero b All diagonal zeros c All entries equal 24 What is a symmetric matrix? a A^T = I b A^T = A c A^T = -A 25 Which operation preserves symmetry of a matrix? a Taking transpose only b Multiplication by a scalar c Non-square multiplication 26 If A is symmetric, A^2 is? a Skew-symmetric b Symmetric c Orthogonal only if special 27 What is the shape rule for AB? a Always square b Inner dimensions must match c Outer dimensions must match 28 Which matrix is invertible if its determinant nonzero? a Non-square matrix b Diagonal with zeros c Any square matrix 29 What is the product AB if A is m x n and B is n x p? a m x p matrix b n x n matrix c p x m matrix 30 What is a zero matrix? a All diagonal ones b All entries are zero c Identity-like with ones 31 Unit matrix is another term for? a Diagonal with ones off-diagonal b Identity matrix c Zero matrix 32 What happens to the determinant under row swap? a Determinant changes sign b Determinant stays same c Determinant doubles 33 Which property is true for A^T? a A^T = -A b (A^T)^T = A c A^T = A 34 If A is orthogonal, A^T = ? a -A^-1 b A c A^-1 35 What is the result of A B if B = I? a AB = B b AB = A c AB = 0 36 The product of two diagonal matrices is? a Zero matrix unless identical b Non-diagonal c Diagonal with products of corresponding entries 37 Which matrix is always square? a Identity matrix b Diagonal with zeros only c Zero matrix 38 What is the transpose of a diagonal matrix? a Also diagonal with same entries b Off-diagonal filled c All zeros 39 What does A^T A preserve for an orthogonal Q? a 0 b Q c I 40 Largest class of matrices closed under addition? a Only diagonal matrices b All same-size matrices c Only square matrices 41 What is the rank relationship under AB? a rank(AB) = rank(A) + rank(B) b rank(AB) > rank(A) c rank(AB) ≤ min(rank(A), rank(B)) 42 Which operation is associative? a Matrix multiplication b Matrix addition c Scalar multiplication not defined 43 Det(A^T) equals? a -Det(A) b Det(A) c Det(A)^2 44 What is a skew-symmetric matrix's diagonal? a Zeros on the diagonal b Arbitrary values c Ones on the diagonal 45 If A is skew-symmetric, what is A^T? a A b -A c A^-1 46 What is a property of diagonal matrices? a Always full rank b Never invertible c Easily computed determinant by product of diagonals 47 What does I A equal? a I A equals I b 0 c A 48 Which matrix is both diagonal and unit? a 0 b A c I 49 What is the result of A + (-A)? a Identity matrix b A^2 c Zero matrix 50 What is the transpose of a sum? a A^T + B^T b A B^T c A^T B^T

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Matrices III Lowersixth Science MathematicsVersión en línea

por YAKILI LMS

What is a skew-symmetric matrix A?

Which property defines an orthogonal matrix Q?

If A and B are square, what is A + B?

Which is true about matrix addition?

What is the result of A + 0 for any matrix A?

What must be true for matrix addition to be defined?

Matrix multiplication is defined for?

What is the product of two diagonal matrices?

What is the identity matrix I?

For a diagonal matrix D, what is D^2?

What is a unit matrix?

Which property does the transpose operation preserve?

What is the transpose of a row vector?

Which operation is not commutative in general?

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

A skew-symmetric matrix A has what property when size odd?

What is the determinant of an odd-order skew-symmetric matrix?

How do you check orthogonality of Q?

What is the effect of multiplying by the identity matrix?

Which is true for matrix addition and scalar multiplication?

If A is m x n and B is n x p, what is AB size?

What is the trace of a diagonal matrix?

A diagonal matrix has what feature?

What is a symmetric matrix?

Which operation preserves symmetry of a matrix?

If A is symmetric, A^2 is?

What is the shape rule for AB?

Which matrix is invertible if its determinant nonzero?

What is the product AB if A is m x n and B is n x p?

What is a zero matrix?

Unit matrix is another term for?

What happens to the determinant under row swap?

Which property is true for A^T?

If A is orthogonal, A^T = ?

What is the result of A B if B = I?

The product of two diagonal matrices is?

Which matrix is always square?

What is the transpose of a diagonal matrix?

What does A^T A preserve for an orthogonal Q?

Largest class of matrices closed under addition?

What is the rank relationship under AB?

Which operation is associative?

Det(A^T) equals?

What is a skew-symmetric matrix's diagonal?

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

What is a property of diagonal matrices?

What does I A equal?

Which matrix is both diagonal and unit?

What is the result of A + (-A)?

What is the transpose of a sum?