WeBWork Linear Algebra - Section 2.2 Properties of Determinants - Section 2.2 Properties of Determinants If A and B are 2 x 2 matrices det(A)=-3

# WeBWork Linear Algebra - Section 2.2 Properties of Determinants

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Section 2.2 Properties of Determinants If A and B are 2 x 2 matrices, det(A)=-3, det(B)=-7, then det(AB)=21 det(-3A)=-27 det(AT)=-3 det(B^-1)=-0.1428 det(B^4)=2401 If the determinant of a 4 x 4 matrix A is the det(A)=4, and the matrix B is obtained from A by multiplying the first row by 2, then det(B)=8 If the determinant of a 4 x 4 matrix A is det(A)=5, and the matrix C is obtained from A by swapping the third and fourth rows, then det(C)=-5 If the determinant of a 5 x 5 matrix A is det(A)=2, and the matrix D is obtained from A by adding 5 times the third row to the second, then det(D)=2 Suppose that a 4 x 4 matrix A with rows v1, v2, v3, and v4 has determinant detA=-8. Find the following determinants: det(v1;v2;v3;4v4]=-32 det[v4;v1;v2;v3]=8 det[v1;v2+3v1;v3;v4]=-8 Subscribe to view the full document. Unformatted text preview: If a 4 x 4 matrix A with rows v1,v2, v3, and v4 had determinant detA=3, then det[v1;9v2+8v4;v3;2v2+5v4]=87 If A and B are n x n matrices, check the true statements below: A. If two row interchanges are made in succession, then the determinant of the new matrix is equal to the determinant of the original matrix. B. If seta is zero, then two rows or two columns are the same, or a row or a column is zero. C. The determinant of A is the product of the diagonal entries in A. D. det(AT)=(-1)det(A) Solution = A Given det[a,b,c;d,e,f,g,h,i]=-1, find the following determinants. det[g,h,i;a,b,c;d,e,f]=-1 det[a,b,c;-7d+a,-7e+b,-7f+c;g,h,i]=7 det[-7d+a,-7e+b,-7f+c;d,e,f;g,h,i]=-1 If B=[1,0,1;-1,1,2;2,2,-2] then det(B^5)=-100000...
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