Matrices IV Lowersixth Further Mathematics

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Test your knowledge on diagonals, determinants and adjugates.

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YAKILI LMS

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Matrices IV Lowersixth Further Mathematics


Matrices IV Lowersixth Further MathematicsOnline version Test your knowledge on diagonals, determinants and adjugates. by YAKILI LMS 1 Nilpotent matrix is the same as the null matrix. Yes No 2 The determinant of a matrix is always positive. Yes No 3 The null space of a singular matrix is nontrivial. Yes No 4 The inverse equals determinant times adj(A). Yes No 5 The inverse of a matrix exists only if determinant is nonzero. Yes No 6 A unit matrix is also called the identity matrix. Yes No 7 A 2x2 matrix with a zero determinant is invertible. Yes No 8 A diagonal matrix is a special case of a square matrix. Yes No 9 A diagonal matrix has nonzero entries only on off-diagonal. Yes No 10 A unit matrix has determinant equal to 1. Yes No 11 A 3x3 determinant cannot be computed by Sarrus. Yes No 12 A 3x3 determinant can be computed using the rule of Sarrus for a 3x3. Yes No 13 A singular matrix has determinant zero. Yes No 14 A matrix is invertible if its determinant is nonzero. Yes No 15 Swapping two rows changes the sign of the determinant. Yes No 16 The determinant of a 2x2 matrix [a b; c d] is ad - bc. Yes No 17 The identity matrix has zeros on the main diagonal. Yes No 18 Swapping rows does not change determinant. Yes No 19 The adjoint of a 3x3 is the inverse of the matrix. Yes No 20 The determinant of a matrix with a row of zeros is zero. Yes No 21 The null matrix has determinant 1. Yes No 22 The determinant of a diagonal matrix is the product of its diagonal entries. Yes No 23 The adjoint of 3x3 involves cofactors of each element. Yes No 24 The determinant of a triangular matrix equals the product of its diagonal entries. Yes No 25 A diagonal matrix is always invertible iff none of its diagonal entries are zero. Yes No 26 Singular matrices have negative determinant. Yes No 27 The adjoint of a matrix is used to compute the inverse: A^{-1} = (1/det A) adj(A). Yes No 28 Row operations do not affect determinant. Yes No 29 The adjoint of a matrix is the transpose of its cofactor matrix. Yes No 30 The determinant of a matrix equals the volume scaling factor of the linear transformation. Yes No 31 A 3x3 determinant can be computed by cofactor expansion along a row. Yes No 32 Expanding along any row or column can compute the determinant. Yes No 33 A diagonal matrix has nonzero entries only on its main diagonal. Yes No 34 A unit matrix has determinant zero. Yes No 35 A matrix with a zero row has a nonzero determinant. Yes No 36 For a diagonal matrix, determinant equals product of diagonal entries. Yes No 37 A 2x2 matrix with rows proportional is singular. Yes No 38 The determinant of a diagonal matrix is the sum of its diagonal entries. Yes No 39 Two rows being equal makes a determinant zero. Yes No 40 The determinant of a diagonal matrix equals the sum of diagonal entries. Yes No 41 A diagonal matrix is a special kind of square matrix. Yes No 42 A matrix with rank equal to its size is invertible. Yes No 43 A null matrix has all entries zero. Yes No 44 Cofactor is just the determinant of the minor, with no sign factor. Yes No 45 The adjoint is the transpose of the inverse. Yes No 46 The adjoint (adjugate) of a 2x2 matrix [[a,b],[c,d]] is [[d,-b],[-c,a]]. Yes No 47 A 2x2 determinant is a + b + c + d. Yes No 48 The determinant of a matrix is equal to the trace. Yes No 49 A square matrix is invertible if its determinant is nonzero. Yes No 50 The determinant of a matrix is always nonnegative. Yes No

Matrices IV Lowersixth Further Mathematics

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Matrices IV Lowersixth Further MathematicsOnline version

by YAKILI LMS

Nilpotent matrix is the same as the null matrix.

The determinant of a matrix is always positive.

The null space of a singular matrix is nontrivial.

The inverse equals determinant times adj(A).

The inverse of a matrix exists only if determinant is nonzero.

A unit matrix is also called the identity matrix.

A 2x2 matrix with a zero determinant is invertible.

A diagonal matrix is a special case of a square matrix.

A diagonal matrix has nonzero entries only on off-diagonal.

A unit matrix has determinant equal to 1.

A 3x3 determinant cannot be computed by Sarrus.

A 3x3 determinant can be computed using the rule of Sarrus for a 3x3.

A singular matrix has determinant zero.

A matrix is invertible if its determinant is nonzero.

Swapping two rows changes the sign of the determinant.

The determinant of a 2x2 matrix [a b; c d] is ad - bc.

The identity matrix has zeros on the main diagonal.

Swapping rows does not change determinant.

The adjoint of a 3x3 is the inverse of the matrix.

The determinant of a matrix with a row of zeros is zero.

The null matrix has determinant 1.

The determinant of a diagonal matrix is the product of its diagonal entries.

The adjoint of 3x3 involves cofactors of each element.

The determinant of a triangular matrix equals the product of its diagonal entries.

A diagonal matrix is always invertible iff none of its diagonal entries are zero.

Singular matrices have negative determinant.

The adjoint of a matrix is used to compute the inverse: A^{-1} = (1/det A) adj(A).

Row operations do not affect determinant.

The adjoint of a matrix is the transpose of its cofactor matrix.

The determinant of a matrix equals the volume scaling factor of the linear transformation.

A 3x3 determinant can be computed by cofactor expansion along a row.

Expanding along any row or column can compute the determinant.

A diagonal matrix has nonzero entries only on its main diagonal.

A unit matrix has determinant zero.

A matrix with a zero row has a nonzero determinant.

For a diagonal matrix, determinant equals product of diagonal entries.

A 2x2 matrix with rows proportional is singular.

The determinant of a diagonal matrix is the sum of its diagonal entries.

Two rows being equal makes a determinant zero.

The determinant of a diagonal matrix equals the sum of diagonal entries.

A diagonal matrix is a special kind of square matrix.

A matrix with rank equal to its size is invertible.

A null matrix has all entries zero.

Cofactor is just the determinant of the minor, with no sign factor.

The adjoint is the transpose of the inverse.

The adjoint (adjugate) of a 2x2 matrix [[a,b],[c,d]] is [[d,-b],[-c,a]].

A 2x2 determinant is a + b + c + d.

The determinant of a matrix is equal to the trace.

A square matrix is invertible if its determinant is nonzero.

The determinant of a matrix is always nonnegative.