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Questions › DSE › DSE 2019 › Q38
0 marksMathematics › Matrices, determinants and linear systems › Determinants and their propertiesModerateabout 2 min

DSE 2019 Question 38: Matrices, determinants and linear systems

Let A=(100210321)A=\begin{pmatrix}1&0&0\\2&1&0\\3&2&1\end{pmatrix}A=​123​012​001​​ and B1,B2,B3B_1,B_2,B_3B1​,B2​,B3​ be three 3×13\times 13×1 column vectors such that AB1=(100)AB_1=\begin{pmatrix}1\\0\\0\end{pmatrix}AB1​=​100​​, AB2=(230)AB_2=\begin{pmatrix}2\\3\\0\end{pmatrix}AB2​=​230​​, AB3=(231)AB_3=\begin{pmatrix}2\\3\\1\end{pmatrix}AB3​=​231​​. Let BBB be the 3×33\times 33×3 matrix whose columns are B1,B2,B3B_1,B_2,B_3B1​,B2​,B3​. Then the determinant det⁡(B)\det(B)det(B) equals:

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Plain-text version

Let A=[1 0 0; 2 1 0; 3 2 1] and B₁,B₂,B₃ be three 3× 1 column vectors such that AB₁=[1; 0; 0], AB₂=[2; 3; 0], AB₃=[2; 3; 1]. Let B be the 3× 3 matrix whose columns are B₁,B₂,B₃. Then the determinant det (B) equals: (A) 3/2 (B) -3/2 (C) 3 (D) -3

Also written as: Let A=[1 0 0; 2 1 0; 3 2 1] and B_1,B_2,B_3 be three 3* 1 column vectors such that AB_1=[1; 0; 0], AB_2=[2; 3; 0], AB_3=[2; 3; 1]. Let B be the 3* 3 matrix whose columns are B_1,B_2,B_3. Then the determinant det (B) equals:

Matrices, determinants and linear systems has come up 102 times in 7 exams since 2006.

What this question tests

This question is on Determinants and their properties, part of Matrices, determinants and linear systems in Mathematics.

Computing determinants and how row and column operations change them.

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